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Book SynopsisMaterials with Rheological Properties presents the evolution of the mathematical models used to calculate the resistance structures and the conditions which enable progress to be made in this field. The author presents equations describing the behavior of each possible type of resistance structure (with discrete collaboration, continuous collaboration and complex composition). These equations are then redefined in the particular concrete form for each type of structure, by using the notions and known parameters from the construction's statics. The mathematical models are then tested using practical case studies.Table of ContentsChapter 1. Introduction 1 1.1. Historical background 1 1.2. Considering the plastic and rheological properties of materials in calculating and designing resistance structures for constructions 3 1.3. The basis of the mathematical model for calculating resistance structures by taking into account the rheological properties of the materials 4 Chapter 2. The Rheological Behavior of Building Materials 9 2.1. Preamble 9 2.2. Structural steel for construction 19 2.2.1. Structural steel for metal construction 19 2.2.2. Reinforcing steel (non-prestressed) 22 2.2.3. Reinforcements, steel wire and steel wire products for prestressed concrete 23 2.3. Concrete 32 Chapter 3. Composite Resistance Structures with Elements Built from Materials Having Different Rheological Properties 45 3.1. Mathematical model for calculating the behavior of composite resistance structures: introduction 45 3.2. Mathematical model for calculating the behavior of composite resistance structures. The formulation considering creep 49 3.2.1. The effects of the long-term actions and loads: overview 49 3.2.1.1. Composite structures with discrete collaboration 61 3.2.1.2. Composite structures with continuous collaboration 67 3.2.1.3. Composite structures with complex composition 80 3.2.2. The effect of repeated short-term variable load actions: overview 86 3.3. Mathematical model for calculating the behavior of composite resistance structures. The formulation considering stress relaxation 95 3.3.1. The effect of long-term actions and loads: overview 95 3.3.1.1. Composite structures with discrete collaboration 102 3.3.1.2. Composite structures with continuous collaboration 106 3.3.1.3. Composite structures with complex composition 115 3.3.2. The effect of repeated short-term variable actions and loads: overview 120 3.4. Conceptual aspects of the mathematical model of resistance structure behavior according to the rheological properties of the materials from which they are made 125 Chapter 4. Applications on Resistance Structures for Constructions 129 4.1. Correction matrix 129 4.1.1. The displacement matrix of the end of a perfectly rigid body due to unit displacements successively applied to the other end of a rigid body 130 4.1.2. The reaction matrix of the end of a perfectly rigid body due to unit forces successively applied to the other end of a rigid body 132 4.2. Calculation of the composite resistance structures. Formulation according to the creep 133 4.2.1. Preliminaries necessary to systematize the calculation of composite structures in the formulation according to the creep 133 4.2.2. Composite structures with discrete collaboration 136 4.2.3. Composite structures with continuous collaboration 140 4.2.4. Composite structures with complex composition 155 4.3. The calculation of composite resistance structures. Formulation according to the stress relaxation 161 4.3.1. Preliminaries necessary to systematize the calculation of the composite structures in the formulation according to the stress relaxation 161 4.3.2. Composite structures with discrete collaboration 165 4.3.3. Composite structures with continuous collaboration 172 4.3.4. Composite structures with complex composition 179 Chapter 5. Numerical Application 189 5.1. Considerations concerning the validation of the mathematical model proposed for estimation through calculation of the behavior of the resistance structures by considering the rheological properties of the materials 189 5.2. The RALUCA computer applications system191 5.3. The resistance structure 198 5.4. Numerical experiments 203 5.4.1. The first series of experiments 203 5.4.1.1. The particular conditions for the analysis of the mathematical model 204 5.4.2. The second series of experiments 206 5.4.2.1. The particular conditions for the analysis of the mathematical model 206 5.4.3. The third series of experiments 211 5.4.3.1. The influence of the parameters defining the creep function 211 5.4.3.2. The stresses state in the structure caused by the contraction of the concrete 214 5.4.3.3. The influence of the deformability of the connection elements on the effort’s distribution among the elements of the structure 217 Appendix 1. The Initial Stresses and Strains State of the Structures with Continuous Collaboration 223 A.1. Simply supported beam with uniformly distributed load 227 A.2. Simply supported beam loaded with a concentrated force 230 A.3. Simply supported beam loaded with a concentrated moment at each end 233 A.4. Simply supported beam loaded with concentrated forces applied eccentrically, acting on a direction parallel with the axis of the beam 235 Appendix 2. Systems of Integral and Integro-differential Equations 241 1. Integro-differential equations whose unknown factors are functions of one variable 242 2. Integro-differential equations whose unknown factors are functions of two variables 251 3. Integro-differential equations whose unknown factors are functions of one or two variables 260 Bibliography 283 Index 287

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Book SynopsisA material's various proprieties is based on its microscopic and nanoscale structures. This book provides an overview of recent advances in computational methods for linking phenomena in systems that span large ranges of time and spatial scales. Particular attention is given to predicting macroscopic properties based on subscale behaviors. Given the book’s extensive coverage of multi-scale methods for modeling both metallic and geologic materials, it will be an invaluable reading for graduate students, scientists, and practitioners alike.Table of ContentsForeword xiii Chapter 1. Accounting for Plastic Strain Heterogenities in Modeling Polycrystalline Plasticity: Microstructure-based Multi-laminate Approaches 1 Patrick FRANCIOSI 1.1. Introduction 1 1.2. Polycrystal morphology in terms of grain and sub-grain boundaries 2 1.2.1. Some evidence of piece-wise regularity for grain boundaries 2 1.2.2. Characteristics of plastic-strain due to sub-grain boundaries 3 1.3. Sub-boundaries and multi-laminate structure for heterogenous plasticity 5 1.3.1. Effective moduli tensor and Green operator of multi-laminate structures 6 1.3.2. Multi-laminate structures and piece-wise homogenous plasticity 10 1.4. Application to polycrystal plasticity within the affine approximation 10 1.4.1. Constitutive relations 10 1.4.2. Fundamental properties for multi-laminate modeling of plasticity 14 1.5. Conclusion 15 1.6. Bibliography 15 Chapter 2. Discrete Dislocation Dynamics: Principles and Recent Applications 17 Marc FIVEL 2.1. Discrete Dislocation Dynamics as a link in multiscale modeling 17 2.2. Principle of Discrete Dislocation Dynamics 19 2.3. Example of scale transition: from DD to Continuum Mechanics 21 2.3.1. Introduction to a dislocation density model 21 2.3.1.1. Constitutive equations of a dislocation based model of crystal plasticity 22 2.3.1.2. Parameter identification 24 2.3.1.3. Application to copper simulations 25 2.3.1.4. Taking into account kinematic hardening 26 2.4. Example of DD analysis: simulations of crack initiation in fatigue 29 2.4.1. Case of single phase AISI 31GL 29 2.5. Conclusions 32 2.6. Bibliography 33 Chapter 3. Multiscale Modeling of Large Strain Phenomenain Polycrystalline Metals 37 Kaan INAL and Raj. K. MISHRA 3.1. Implementation of polycrystal plasticity in finite element analysis 39 3.2. Kinematics and constitutive framework 41 3.3. Forward Euler algorithm 44 3.4. Validation of the forward Euler algorithm 46 3.5. Time step issues in the forward Euler scheme 49 3.6. Comparisons of CPU times: the rate tangent versus the forward Euler methods 51 3.7. Conclusions 52 3.8. Acknowledgements 52 3.9. Bibliography 52 Chapter 4. Earth Mantle Rheology Inferred from Homogenization Theories 55 Olivier CASTELNAU, Ricardo LEBENSOHN, Pedro Ponte CASTAÑEDA and Donna BLACKMAN 4.1. Introduction 55 4.2. Grain local behavior 57 4.3. Full-field reference solutions 59 4.4. Mean-field estimates 62 4.4.1. Basic features of mean-field theories 62 4.4.2. Results 64 4.5. Concluding observations 66 4.6. Bibliography 68 Chapter 5. Modeling Plastic Anistropy and Strength Differential Effects in Metallic Materials 71 Oana CAZACU and Frédéric BARLAT 5.1. Introduction 71 5.2. Isotropic yield criteria 72 5.2.1. Pressure insensitive materials deforming by slip 72 5.2.2. Pressure insensitive materials deforming by twinning 73 5.2.3. Pressure insensitive materials with non-Schmid effects 76 5.2.4. Pressure sensitive materials 78 5.2.5. SD effect and plastic flow 80 5.3. Anisotropic yield criteria with SD effects 80 5.3.1. Cazacu and Barlat [CAZ 04] orthotropic yield criterion 80 5.3.2. Cazacu Plunkett Barlat yield criterion [CAZ 06] 82 5.4. Modeling anisotropic hardening due to texture evolution 83 5.5. Conclusions and future perspectives 86 5.6. Bibliography 87 Chapter 6. Shear Bands in Steel Plates under Impact Loading 91 George Z. VOYIADJIS and Amin H. ALMASRI 6.1. Introduction 91 6.2. Viscoplasticity and constitutive modeling 92 6.3. Higher order gradient theory 97 6.4. Two-dimensional plate subjected to velocity boundary conditions 102 6.5. Shear band in steel plate punch 105 6.6. Conclusions 108 6.7. Bibliography 109 Chapter 7. Viscoplastic Modeling of Anisotropic Textured Metals 111 Brian PLUNKETT and Oana CAZACU 7.1. Introduction 111 7.2. Anisotropic elastoviscoplastic model 113 7.3. Application to zirconium. 115 7.3.1. Quasi-static deformation of zirconium 115 7.3.2. High strain-rate deformation of zirconium 120 7.4. High strain-rate deformation of tantalum 124 7.5. Conclusions125 7.6. Bibliography 126 Chapter 8. Non-linear Elastic Inhomogenous Materials: Uniform Strain Fields and Exact Relations 129 Qi-Chang HE, B. BARY and Hung LE QUANG 8.1. Introduction 129 8.2. Locally uniform strain fields 130 8.3. Exact relations for the effective elastic tangent moduli 136 8.4. Cubic polycrystals 139 8.5. Power-law fibrous composites 144 8.6. Conclusion 149 8.7. Bibliography 149 Chapter 9. 3D Continuous and Discrete Modeling of Bifurcations in Geomaterials 153 Florent PRUNIER, Félix DARVE, Luc SIBILLE and François NICOT 9.1. Introduction 153 9.2. 3D bifurcations exhibited by an incrementally non-linear constitutive relation 155 9.2.1. Incrementally non-linear and piecewise linear relations 155 9.2.2. 3D analysis of the second-order work with phenomenological constitutive models 157 9.3. Discrete modeling of the failure mode related to second-order work criterion 165 9.4. Conclusions 173 9.5. Acknowledgements 174 9.6. Bibliography 174 Chapter 10. Non-linear Micro-cracked Geomaterials: Anisotropic Damage and Coupling with Plasticity 177 Djimédo KONDO, Qizhi ZHU, Vincent MONCHIET and Jian-Fu SHAO 10.1. Introduction 177 10.2. Anisotropic elastic damage model with unilateral effects 179 10.2.1. Homogenization of elastic micro-cracked media 179 10.2.1.1. Micromechanics of media with random microstructure 179 10.2.1.2. Application to micro-cracked media 180 10.2.2. Micro-crack closure condition and damage evolution 181 10.2.2.1. Micro-crack closure effects and unilateral damage 181 10.2.2.2. Damage criterion and evolution law 182 10.2.3. Non-local micromechanics-based damage model 183 10.2.4. Application of the model 184 10.2.4.1. Uniaxial tensile tests 184 10.2.4.2. Predictions of the anisotropic damage model for William’s test 185 10.2.4.3. Numerical analysis of Hassanzadeh’s direct tension test 188 10.3. A new model for ductile micro-cracked materials 188 10.3.1. Introductory observations 188 10.3.2. Basic concepts and methodology of the limit analysis approach 190 10.3.2.1. Representative volume element with oblate voids 190 10.3.2.2. The Eshelby-like velocity field 191 10.3.3. Determination of the macroscopic yield surface 192 10.3.3.1. The question of the boundary conditions 192 10.3.3.2. Principle of the determination of the yield function 193 10.3.3.3. Closed form expression of the macroscopic yield function 193 10.3.4. The particular case of penny-shaped cracks 195 10.4. Conclusions 197 10.5. Acknowledgement 198 10.6. Appendix 198 10.7. Bibliography 198 Chapter 11. Bifurcation in Granular Materials: A Multiscale Approach 203 François NICOT, Luc SIBILLE and Félix DARVE 11.1. Introduction 203 11.2. Microstructural origin of the vanishing of the second-order work 205 11.2.1. The micro-directional model 205 11.2.2. Microstructural expression of the macroscopic second-order work 206 11.2.3. From micro to macro second-order work 208 11.2.4. Micromechanical analysis of the vanishing of the second-order work 210 11.3. Some remarks on the basic micro-macro relation for the second-order work 212 11.4. Conclusion 213 11.5. Bibliography 214 Chapter 12. Direct Scale Transition Approach for Highly-filled Viscohyperelastic Particulate Composites: Computational Study 215 Carole NADOT-MARTIN, Marion TOUBOUL, André DRAGON and Alain FANGET 12.1. Morphological approach in the finite strain framework 216 12.1.1. Geometric schematization 216 12.1.2. Localization-homogenization problem 217 12.1.2.1. Principal tools and stages 217 12.1.2.2. Solving procedure 219 12.2. Evaluation involving FEM/MA confrontations 221 12.2.1. Material geometry, relative representations 221 12.2.2. Loading paths, methodology of analysis 223 12.2.3. MA estimates compared to FEM results for hyperelastic constituents 225 12.2.4. Evaluation involving viscohyperelastic behavior of the matrix 229 12.3. Conclusions and prospects 232 12.4. Bibliography 234 Chapter 13. A Modified Incremental Homogenization Approach for Non-linear Behaviors of Heterogenous Cohesive Geomaterials 237 Ariane ABOU-CHAKRA GUÉRY, Fabrice CORMERY, Jian-Fu SHAO and Djimédo KONDO 13.1. Introduction 237 13.2. Experimental observations on the Callovo-Oxfordian argillite behavior 238 13.2.1. Microstructure and mineralogical composition of the material 238 13.2.2. Brief summary of the macroscopic behavior of the material 239 13.3. Incremental formulation of the homogenized constitutive relation 240 13.3.1. Introduction 240 13.3.2. Limitations of Hill’s incremental method 242 13.3.3. Modified Hill’s incremental method 243 13.4. Modifying of the local constituents’ behaviors 244 13.4.1. Elastoplastic behavior of the clay phase 244 13.4.2. Elastic unilateral damage behavior of the calcite phase 245 13.5. Implementation and numerical validation of the model 247 13.5.1. Local integration of the micromechanical model 247 13.5.2. Comparison with unit cell (finite element) calculation 248 13.6. Calibration and experimental validations of the modified incremental micromechanical model 248 13.7. Conclusions 249 13.8. Acknowledgement 251 13.9. Bibliography 251 Chapter 14. Meso- to Macro-scale Probability Aspects for Size Effects and Heterogenous Materials Failure 253 Jean-Baptiste COLLIAT, Martin HAUTEFEUILLE and Adnan IBRAHIMBEGOVIC 14.1. Introduction 253 14.2. Meso-scale deterministic model 254 14.2.1. Structured meshes and kinematic enhancements 255 14.2.2. Operator split solution for interface failure 257 14.2.3. Comparison between structured and unstructured mesh approach 258 14.3. Probability aspects of inelastic localized failure for heterogenous materials 259 14.3.1. Meso-scale geometry description 260 14.3.2. Stochastic integration 261 14.4. Results of the probabilistic characterization of the two phase material 263 14.4.1. Determination of SRVE size 263 14.4.2. Numerical results and discussion 264 14.5. Size effect modeling 266 14.5.1. Random fields and the Karhunen-Loeve expansion 267 14.5.2. Size effect and correlation length 269 14.6. Conclusion 271 14.7. Acknowledgments 272 14.8. Bibliography 272 Chapter 15. Damage and Permeability in Quasi-brittle Materials: from Diffuse to Localized Properties 277 Gilles PIJAUDIER-CABOT, Frédéric DUFOUR and Marta CHOINSKA 15.1. Introduction 277 15.2. Mechanical problem – continuum damage modeling 279 15.3. Permeability matching law 281 15.3.1. Diffuse damage 281 15.3.2. Localized damage – crack opening versus permeability 281 15.3.3. Matching law 283 15.4. Calculation of a crack opening in continuum damage calculations 283 15.5. Structural simulations 286 15.5.1. Mechanical problem – Brazilian splitting test 287 15.5.2. Evolution of apparent permeability 289 15.6. Conclusions 291 15.7. Acknowledgement 291 15.8. Bibliography 291 Chapter 16. A Multiscale Modeling of Granular Materials with Surface Energy Forces 293 Pierre-Yves HICHER and Ching S. CHANG 16.1. Introduction 293 16.2. Stress-strain model 294 16.2.1. Inter-particle behavior 296 16.2.1.1. Elastic part 296 16.2.1.2. Plastic part 296 16.2.1.3. Interlocking influence 297 16.2.1.4. Elastoplastic force-displacement relationship 298 16.2.2. Stress-strain relationship 298 16.2.2.1. Micro-macro relationship 298 16.2.2.2. Calculation scheme 300 16.2.3. Summary of parameters 301 16.3. Results of numerical simulation without surface energy forces consideration 302 16.4. Granular material with surface energy forces: the example of lunar soil 306 16.4.1. Van der Waals forces 308 16.4.2. Triaxial tests with consideration of surface energy forces 311 16.5. Summary and conclusion 314 16.6. Bibliography 315 Chapter 17. Length Scales in Mechanics of Granular Solids 319 Farhang RADJAI 17.1. Introduction 319 17.2. Model description 320 17.3. Force chains 321 17.3.1. Probability density functions 321 17.3.2. Bimodal character of stress transmission 322 17.3.3. Spatial correlations 324 17.4. Fluctuating particle displacements 325 17.4.1. Uniform strain and fluctuations 325 17.4.2. Scale-dependent pdfs 326 17.4.3. Spatial correlations 328 17.4.4. Granulence 329 17.5. Friction mobilization 330 17.5.1. Critical contacts 330 17.5.2. Evolution of critical contacts 330 17.5.3. Spatial correlations 331 17.6. Conclusion 332 17.7. Acknowledgements 333 17.8. Bibliography 333 List of Authors 337 Index 341

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Book SynopsisThis book examines the phenomena of fluid flow and transfer as governed by mechanics and thermodynamics. Part 1 concentrates on equations coming from balance laws and also discusses transportation phenomena and propagation of shock waves. Part 2 explains the basic methods of metrology, signal processing, and system modeling, using a selection of examples of fluid and thermal mechanics.Table of ContentsPreface xi Chapter 1. Thermodynamics of Discrete Systems 1 1.1. The representational bases of a material system 1 1.1.1. Introduction 1 1.1.2. Systems analysis and thermodynamics 8 1.1.3. The notion of state 11 1.1.4. Processes and systems 13 1.2. Axioms of thermostatics 15 1.2.1. Introduction 15 1.2.2. Extensive quantities 16 1.2.3. Energy, work and heat 20 1.3. Consequences of the axioms of thermostatics 21 1.3.1. Intensive variables 21 1.3.2. Thermodynamic potentials 23 1.4. Out-of-equilibrium states 29 1.4.1. Introduction 29 1.4.2. Discontinuous systems 30 1.4.3. Application to heat engines 45 Chapter 2. Thermodynamics of Continuous Media 47 2.1. Thermostatics of continuous media 47 2.1.1. Reduced extensive quantities 47 2.1.2. Local thermodynamic equilibrium 48 2.1.3. Flux of extensive quantities 50 2.1.4. Balance equations in continuous media 54 2.1.5. Phenomenological laws 57 2.2. Fluid statics 63 2.2.1. General equations of fluid statics 63 2.2.2. Pressure forces on solid boundaries 68 2.3. Heat conduction 72 2.3.1. The heat equation 72 2.3.2. Thermal boundary conditions 72 2.4. Diffusion 73 2.4.1. Introduction 73 2.4.2. Molar and mass fluxes 77 2.4.3. Choice of reference frame 80 2.4.4. Binary isothermal mixture 85 2.4.5. Coupled phenomena with diffusion 97 2.4.6. Boundary conditions 99 Chapter 3. Physics of Energetic Systems in Flow 101 3.1. Dynamics of a material point 101 3.1.1. Galilean reference frames in traditional mechanics 101 3.1.2. Isolated mechanical system and momentum 102 3.1.3. Momentum and velocity 103 3.1.4. Definition of force 104 3.1.5. The fundamental law of dynamics (closed systems) 106 3.1.6. Kinetic energy 106 3.2. Mechanical material system 107 3.2.1. Dynamic properties of a material system 107 3.2.2. Kinetic energy of a material system 109 3.2.3. Mechanical system in thermodynamic equilibrium the rigid solid 111 3.2.4. The open mechanical system 112 3.2.5. Thermodynamics of a system in motion 116 3.3. Kinematics of continuous media 119 3.3.1. Lagrangian and Eulerian variables 119 3.3.2. Trajectories, streamlines, streaklines 121 3.3.3. Material (or Lagrangian) derivative 122 3.3.4. Deformation rate tensors 129 3.4. Phenomenological laws of viscosity 132 3.4.1. Definition of a fluid 132 3.4.2. Viscometric flows 135 3.4.3. The Newtonian fluid 146 Chapter 4. Fluid Dynamics Equations 151 4.1. Local balance equations 151 4.1.1. Balance of an extensive quantity G 151 4.1.2. Interpretation of an equation in terms of the balance equation 153 4.2. Mass balance 154 4.2.1. Conservation of mass and its consequences 154 4.2.2. Volume conservation 160 4.3. Balance of mechanical and thermodynamic quantities 160 4.3.1. Momentum balance 160 4.3.2. Kinetic energy theorem 164 4.3.3. The vorticity equation 171 4.3.4. The energy equation 172 4.3.5. Balance of chemical species 177 4.4. Boundary conditions 178 4.4.1. General considerations 178 4.4.2. Geometric boundary conditions 179 4.4.3. Initial conditions 181 4.5. Global form of the balance equations 182 4.5.1. The interest of the global form of a balance 182 4.5.2. Equation of mass conservation 184 4.5.3. Volume balance 184 4.5.4. The momentum flux theorem 184 4.5.5. Kinetic energy theorem 186 4.5.6. The energy equation 187 4.5.7. The balance equation for chemical species 188 4.6. Similarity and non-dimensional parameters 189 4.6.1. Principles 189 Chapter 5. Transport and Propagation 199 5.1. General considerations 199 5.1.1. Differential equations 199 5.1.2. The Cauchy problem for differential equations 202 5.2. First order quasi-linear partial differential equations 203 5.2.1. Introduction 203 5.2.2. Geometric interpretation of the solutions 204 5.2.3. Comments 206 5.2.4. The Cauchy problem for partial differential equations 206 5.3. Systems of first order partial differential equations 207 5.3.1. The Cauchy problem for n unknowns and two variables 207 5.3.2. Applications in fluid mechanics 210 5.3.3. Cauchy problem with n unknowns and p variables 216 5.3.4. Partial differential equations of order n 218 5.3.5. Applications 220 5.3.6. Physical interpretation of propagation 223 5.4. Second order partial differential equations 225 5.4.1. Introduction 225 5.4.2. Characteristic curves of hyperbolic equations 226 5.4.3. Reduced form of the second order quasi-linear partial differential equation 229 5.4.4. Second order partial differential equations in a finite domain 232 5.4.5. Second order partial differential equations and their boundary conditions 233 5.5. Discontinuities: shock waves 239 5.5.1. General considerations 239 5.5.2. Unsteady 1D flow of an inviscid compressible fluid 239 5.5.3. Plane steady supersonic flow 244 5.5.4. Flow in a nozzle 244 5.5.5. Separated shock wave 248 5.5.6. Other discontinuity categories 248 5.5.7. Balance equations across a discontinuity 249 5.6. Some comments on methods of numerical solution 250 5.6.1. Characteristic curves and numerical discretization schemes 250 5.6.2. A complex example 253 5.6.3. Boundary conditions of flow problems 255 Chapter 6. General Properties of Flows 257 6.1. Dynamics of vorticity 257 6.1.1. Kinematic properties of the rotation vector 257 6.1.2. Equation and properties of the rotation vector 261 6.2. Potential flows 269 6.2.1. Introduction 269 6.2.2. Bernoulli’s second theorem 269 6.2.3. Flow of compressible inviscid fluid 270 6.2.4. Nature of equations in inviscid flows 271 6.2.5. Elementary solutions in irrotational flows 273 6.2.6. Surface waves in shallow water 284 6.3. Orders of magnitude 288 6.3.1. Introduction and discussion of a simple example 288 6.3.2. Obtaining approximate values of a solution 291 6.4. Small parameters and perturbation phenomena 296 6.4.1. Introduction 296 6.4.2. Regular perturbation 296 6.4.3. Singular perturbations 305 6.5. Quasi-1D flows 309 6.5.1. General properties 309 6.5.2. Flows in pipes 314 6.5.3. The boundary layer in steady flow 319 6.6. Unsteady flows and steady flows 327 6.6.1. Introduction 327 6.6.2. The existence of steady flows 328 6.6.3. Transitional regime and permanent solution 330 6.6.4. Non-existence of a steady solution 334 Chapter 7. Measurement, Representation and Analysis of Temporal Signals 339 7.1. Introduction and position of the problem 339 7.2. Measurement and experimental data in flows 340 7.2.1. Introduction 340 7.2.2. Measurement of pressure 341 7.2.3. Anemometric measurements 342 7.2.4. Temperature measurements 346 7.2.5. Measurements of concentration 347 7.2.6. Fields of quantities and global measurements 347 7.2.7. Errors and uncertainties of measurements 351 7.3. Representation of signals 357 7.3.1. Objectives of continuous signal representation 357 7.3.2. Analytical representation 360 7.3.3. Signal decomposition on the basis of functions; series and elementary solutions 361 7.3.4. Integral transforms 363 7.3.5. Time-frequency (or timescale) representations 374 7.3.6. Discretized signals 381 7.3.7. Data compression 385 7.4. Choice of representation and obtaining pertinent information 389 7.4.1. Introduction 389 7.4.2. An example: analysis of sound 390 7.4.3. Analysis of musical signals 393 7.4.4. Signal analysis in aero-energetics 402 Chapter 8. Thermal Systems and Models 405 8.1. Overview of models 405 8.1.1. Introduction and definitions 405 8.1.2. Modeling by state representation and choice of variables 408 8.1.3. External representation 410 8.1.4. Command models 411 8.2. Thermodynamics and state representation 412 8.2.1. General principles of modeling 412 8.2.2. Linear time-invariant system (LTIS) 420 8.3. Modeling linear invariant thermal systems 422 8.3.1. Modeling discrete systems 422 8.3.2. Thermal models in continuous media 431 8.4. External representation of linear invariant systems 446 8.4.1. Overview 446 8.4.2. External description of linear invariant systems 446 8.5. Parametric models 451 8.5.1. Definition of model parameters 451 8.5.2. Established regimes of linear invariant systems 453 8.5.3. Established regimes in continuous media 458 8.6. Model reduction 465 8.6.1. Overview 465 8.6.2. Model reduction of discrete systems 466 8.7. Application in fluid mechanics and transfer in flows 474 Appendix 1. Laplace Transform 477 A1.1. Definition 477 A1.2. Properties 477 A1.3. Some Laplace transforms 478 A1.4. Application to the solution of constant coefficient differential equations 479 Appendix 2. Hilbert Transform 481 Appendix 3. Cepstral Analysis 483 A3.1. Introduction 483 A3.2. Definitions 483 A3.3. Example of echo suppression 484 A3.4. General case 485 Appendix 4. Eigenfunctions of an Operator 487 A4.1. Eigenfunctions of an operator 487 A4.2. Self-adjoint operator 487 A4.2.1. Eigenfunctions 487 A4.2.2. Expression of a function of f using an eigenfunction basis-set 488 Bibliography 489 Index 497

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Book SynopsisOver the last 50 years, the various available methods of investigating dynamic properties of materials have resulted in significant advances in this area of materials science. Dynamic tests have also recently proven to be as efficient as static tests, and have the advantage that they are often easier to use at lower frequency. This book explores dynamic testing, the methods used, and the experiments performed, placing a particular emphasis on the context of bounded medium elastodynamics. The book initially focuses on the complements of continuum mechanics before moving on to the various types of rod vibrations: extensional, bending and torsional. In addition, chapters contain practical examples alongside theoretical discussion to facilitate the reader's understanding. The results presented are the culmination of over 30 years of research by the authors and will be of great interest to anyone involved in this field.Table of ContentsPreface xix Acknowledgements xxix Part A Constitutive Equations of Materials 1 Chapter 1 Elements of Anisotropic Elasticity and Complements on Previsional Calculations 3Yvon CHEVALIER 1.1 Constitutive equations in a linear elastic regime 4 1.2 Technical elastic moduli 7 1.3 Real materials with special symmetries 10 1.4 Relationship between compliance Sij and stiffness Cij for orthotropic materials 23 1.5 Useful inequalities between elastic moduli 24 1.6 Transformation of reference axes is necessary in many circumstances 27 1.7 Invariants and their applications in the evaluation of elastic constants 28 1.8 Plane elasticity 35 1.9 Elastic previsional calculations for anisotropic composite materials 38 1.10 Bibliography 51 1.11 Appendix 52 Appendix 1.A Overview on methods used in previsional calculation of fiber-reinforced composite materials 52 Chapter 2 Elements of Linear Viscoelasticity 57Yvon CHEVALIER 2.1 Time delay between sinusoidal stress and strain 59 2.2 Creep and relaxation tests 60 2.3 Mathematical formulation of linear viscoelasticity 63 2.4 Generalization of creep and relaxation functions to tridimensional constitutive equations 71 2.5 Principle of correspondence and Carson-Laplace transform for transient viscoelastic problems 74 2.6 Correspondence principle and the solution of the harmonic viscoelastic system 82 2.7 Inter-relationship between harmonic and transient regimes 83 2.8 Modeling of creep and relaxation functions: example 87 2.9 Conclusion 100 2.10 Bibliography 100 Chapter 3 Two Useful Topics in Applied Viscoelasticity: Constitutive Equations for Viscoelastic Materials 103Yvon CHEVALIER and Jean Tuong VINH 3.1 Williams-Landel-Ferry’s method 104 3.2 Viscoelastic time function obtained directly from a closed-form expression of complex modulus or complex compliance 112 3.3 Concluding remarks 136 3.4 Bibliography 137 3.5 Appendices 139 Appendix 3.A Inversion of Laplace transform 139 Appendix 3.B Sutton’s method for long time response 143 Chapter 4 Formulation of Equations of Motion and Overview of their Solutions by Various Methods 145Jean Tuong VINH 4.1 D’Alembert’s principle 146 4.2 Lagrange’s equation 149 4.3 Hamilton’s principle 157 4.4 Practical considerations concerning the choice of equations of motion and related solutions 159 4.5 Three-, two- or one-dimensional equations of motion? 162 4.6 Closed-form solutions to equations of motion 163 4.7 Bibliography 164 4.8 Appendices 165 Appendix 4.A Equations of motion in elastic medium deduced from Love’s variational principle 165 Appendix 4.B Lagrange’s equations of motion deduced from Hamilton’s principle 167 Part B Rod Vibrations 173 Chapter 5 Torsional Vibration of Rods 175Yvon CHEVALIER, Michel NUGUES and James ONOBIONO 5.1 Introduction 175 5.1.1 Short bibliography of the torsion problem 176 5.1.2 Survey of solving methods for torsion problems 176 5.1.3 Extension of equations of motion to a larger frequency range 179 5.2 Static torsion of an anisotropic beam with rectangular section without bending – Saint Venant, Lekhnitskii’s formulation 180 5.3 Torsional vibration of a rod with finite length 199 5.4 Simplified boundary conditions associated with higher approximation equations of motion [5.49] 204 5.5 Higher approximation equations of motion 205 5.6 Extension of Engström’s theory to the anisotropic theory of dynamic torsion of a rod with rectangular cross-section 207 5.7 Equations of motion 212 5.8 Torsion wave dispersion 215 5.9 Presentation of dispersion curves 219 5.10 Torsion vibrations of an off-axis anisotropic rod 225 5.11 Dispersion of deviated torsional waves in off-axis anisotropic rods with rectangular cross-section 235 5.12 Dispersion curve of torsional phase velocities of an off-axis anisotropic rod 240 5.13 Concluding remarks 241 5.14 Bibliography 242 5.15 Table of symbols 244 5.16 Appendices 246 Appendix 5.A Approximate formulae for torsion stiffness 246 Appendix 5.B Equations of torsional motion obtained from Hamilton’s variational principle 250 Appendix 5.C Extension of Barr’s correcting coefficient in equations of motion 257 Appendix 5.D Details on coefficient calculations for θ (z, t) and ζ (z, t) 258 Appendix 5.E A simpler solution to the problem analyzed in Appendix 5.D 263 Appendix 5.F Onobiono’s and Zienkievics’ solutions using finite element method for warping function φ 265 Appendix 5.G Formulation of equations of motion for an off-axis anisotropic rod submitted to coupled torsion and bending vibrations 273 Appendix 5.H Relative group velocity versus relative wave number 279 Chapter 6 Bending Vibration of a Rod 291Dominique LE NIZHERY 6.1 Introduction 291 6.1.1 Short bibliography of dynamic bending of a beam 292 6.2 Bending vibration of straight beam by elementary theory 293 6.3 Higher approximation theory of bending vibration 299 6.4 Bending vibration of an off-axis anisotropic rod 313 6.5 Concluding remarks 324 6.6 Bibliography 326 6.7 Table of symbols 327 6.8 Appendices 328 Appendix 6.A Timoshenko’s correcting coefficients for anisotropic and isotropic materials 328 Appendix 6.B Correcting coefficient using Mindlin’s method 333 Appendix 6.C Dispersion curves for various equations of motion 334 Appendix 6.D Change of reference axes and elastic coefficients for an anisotropic rod 337 Chapter 7 Longitudinal Vibration of a Rod 339Yvon CHEVALIER and Maurice TOURATIER 7.1 Presentation 339 7.2 Bishop’s equations of motion 343 7.3 Improved Bishop’s equation of motion 345 7.4 Bishop’s equation for orthotropic materials 346 7.5 Eigenfrequency equations for a free-free rod 346 7.6 Touratier’s equations of motion of longitudinal waves 350 7.7 Wave dispersion relationships 367 7.8 Short rod and boundary conditions 393 7.9 Concluding remarks about Touratier’s theory 395 7.10 Bibliography 396 7.11 List of symbols 397 7.12 Appendices 399 Appendix 7.A an outline of some studies on longitudinal vibration of rods with rectangular cross-section 399 Appendix 7.B Formulation of Bishop’s equation by Hamilton’s principle by Rao and Rao 401 Appendix 7.C Dimensionless Bishop’s equations of motion and dimensionless boundary conditions 405 Appendix 7.D Touratier’s equations of motion by variational calculus 408 Appendix 7.E Calculation of correcting factor q (Cijkl) 409 Appendix 7.F Stationarity of functional J and boundary equations 419 Appendix 7.G On the possible solutions of eigenvalue equations 419 Chapter 8 Very Low Frequency Vibration of a Rod by Le Rolland-Sorin’s Double Pendulum 425Mostefa ARCHI and Jean-Baptiste CASIMIR 8.1 Introduction 425 8.2 Short bibliography 427 8.3 Flexural vibrations of a rod using coupled pendulums 427 8.4 Torsional vibration of a beam by double pendulum 434 8.5 Complex compliance coefficient of viscoelastic materials 436 8.6 Elastic stiffness of an off-axis rod 443 8.7 Bibliography 449 8.8 List of symbols 450 8.9 Appendices 452 Appendix 8.A Closed-form expression of θ1 or θ2 oscillation angles of the pendulums and practical considerations 452 Appendix 8.B Influence of the highest eigenfrequency ω3 on the pendulum oscillations in the expression of θ1 (t) 457 Appendix 8.C Coefficients a of compliance matrix after a change of axes for transverse isotropic material 458 Appendix 8.D Mathematical formulation of the simultaneous bending and torsion of an off-axis rectangular rod 460 Appendix 8.E Details on calculations of s35 and ϑ13 of transverse isotropic materials 486 Chapter 9 Vibrations of a Ring and Hollow Cylinder 493Jean Tuong VINH 9.1 Introduction 493 9.2 Equations of motion of a circular ring with rectangular cross-section 494 9.3 Bibliography 502 9.4 Appendices 503 Appendix 9.A Expression u (θ) in the three subintervals delimited by the roots of equation [9.33] 503 Chapter 10 Characterization of Isotropic and Anisotropic Materials by Progressive Ultrasonic Waves 513Patrick GARCEAU 10.1 Presentation of the method 513 10.2 Propagation of elastic waves in an infinite medium 515 10.3 Progressive plane waves 516 10.4 Polarization of three kinds of waves 518 10.5 Propagation in privileged directions and phase velocity calculations 519 10.6 Slowness surface and wave propagation through a separation surface 528 10.7 Propagation of an elastic wave through an anisotropic blade with two parallel faces 535 10.8 Concluding remarks 542 10.9 Bibliography 543 10.10 List of Symbols 544 10.11 Appendices 546 Appendix 10.A Energy velocity, group velocity, Poynting vector 546 Appendix 10.B Slowness surface and energy velocity 553 Chapter 11 Viscoelastic Moduli of Materials Deduced from Harmonic Responses of Beams 555Tibi BEDA, Christine ESTEOULE, Mohamed SOULA and Jean Tuong VINH 11.1 Introduction 555 11.2 Guidelines for practicians 557 11.3 Solution of a viscoelastic problem using the principle of correspondence 558 11.4 Viscoelastic solution of equation of motions 564 11.5 Viscoelastic moduli using equations of higher approximation degree 579 11.6 Bibliography 588 11.7 Appendices 589 Appendix 11.A Transmissibility function of a rod submitted to longitudinal vibration (elementary equation of motion) 589 Appendix 11.B Newton-Raphson’s method applied to a couple of functions of two real variables 1 and 2 components of 590 Appendix 11.C Transmissibility function of a clamped-free Bernoulli’s rod submitted to bending vibration 591 Appendix 11.D Complex transmissibility function of a clamped-free Bernoulli’s rod and its decomposition into two functions of real variables 593 Appendix 11.E Eigenvalue equation of clamped-free Timoshenko’s rod 594 Appendix 11.F Transmissibility function of clamped-free Timoshenko’s rod 595 Chapter 12 Continuous Element Method Utilized as a Solution to Inverse Problems in Elasticity and Viscoelasticity 599Jean-Baptiste CASIMIR 12.1 Introduction 599 12.2 Overview of the continuous element method 601 12.3 Boundary conditions and their implications in the transfer matrix 608 12.4 Extensional vibration of straight beams (elementary theory) 609 12.5 The direct problem of beams submitted to bending vibration 612 12.6 Successive calculation steps to obtain a transfer matrix and simple displacement transfer function 620 12.7 Continuous element method adapted for solving an inverse problem in elasticity and viscoelasticity 622 12.8 Bibliography 624 12.9 Appendices 624 Appendix 12.A Wavenumbers deduced from Timoshenko’s equation 624 List of Authors 629 Index 631

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Book SynopsisThis book covers a wide range of topics that address the main areas of interest to scientists, engineers, and students concerned with the synthesis, characterization and applications of nanomaterials. Development techniques, properties, and examples of industrial applications are all widely represented as they apply to various nanostructured materials including nanocomposites and multilayered nanometric coatings. The book also illustrates a wide range of powerful methods of nanomaterial/nanostructure synthesis such as microwave-assisted methods, pulsed electrodeposition, ion beams, or glancing angle deposition. Techniques for the encapsulation and functionalization of nanoparticles, as well as the adhesion and mechanical characterization of nanostructured thin films, are also described and discussed. It is to be recommended to anyone working in the field of nanomaterials, especially in connection with the functionalization and engineering of surfaces.Trade Review"The book is interesting and useful for readers working in the nanosciences . . . however, overall the book can be easily understood by students, researchers and teachers in the area of optics." (Optics and Photonics News, 18 May 2011)Table of ContentsPreface xv Jamal TAKADOUM Chapter 1. Architecture of Thin Solid Films by the GLAD Technique 1 Nicolas MARTIN, Kevin ROBBIE and Luc CARPENTIER 1.1. Introduction 1 1.2. The GLAD technique 2 1.3. Resulting properties 8 1.4. Conclusions and outlooks 23 1.5. Bibliography 24 Chapter 2. Transparent Polymer Nanocomposites: A New Class of Functional Materials 31 Anne CHRISTMANN, Claire LONGUET and José-Marie LOPEZ CUESTA 2.1. Introduction 31 2.2. Nanoparticle modifications 32 2.3. Nanoparticles and nanocomposites 39 2.4. Conclusion 45 2.5. Bibliography 47 Chapter 3. Nanostructures by Ion Irradiation 53 Jean-Claude PIVIN 3.1. Introduction 53 3.2. Physical bases 55 3.3. Nanostructures produced in ballistic regime 59 3.4. Nanostructures produced in electronic slowing down regime 68 3.5. Conclusions 76 3.6. Appendix: basic formula of ion stopping 77 3.7. Bibliography 82 Chapter 4. Microencapsulation 89 Claude ROQUES-CARMES and Christine MILLOT 4.1. Introduction 89 4.2. The processes of microencapsulation 91 4.3. Kinetics of release 100 4.4. Conclusion 105 4.5. Bibliography 107 Chapter 5. Decorative PVD Coatings 109 Raymond CONSTANTIN, Pierre-Albert STEINMANN and Christian MANASTERSKI 5.1. Introduction 109 5.2. Concept of color 110 5.3. Representation and measurement of color 112 5.4. Golden PVD coatings 113 5.5. Gray color PVD coatings 132 5.6. Black color PVD coatings 138 5.7. Blue color PVD coatings 145 5.8. PVD coatings with interferential color 145 5.9. Decorative PVD coatings and corrosion resistance 150 5.10. Bibliography 155 Chapter 6. Microwave Chemistry and Nanomaterials: From Laboratory to Pilot Plant 163 Didier STUERGA and Thierry CAILLOT 6.1. Introduction 163 6.2. General context 163 6.3. Microwave nanomaterials: from single oxides to metallic clusters 167 6.4. Microwave and inorganic condensation processes 182 6.5. The RAMO system and the MIT process 186 6.6. From laboratory to pilot 191 6.7. Bibliography 192 Chapter 7. Aluminum-Based Nanostructured Coatings Deposited by Magnetron Sputtering for Corrosion Protection of Steels 207 Frédéric SANCHETTE, Cédric DUCROS and Alain BILLARD 7.1. Introduction 207 7.2. Aluminum-based nanostructured coatings deposited by magnetron sputtering for corrosion protection of steels 208 7.3. Conclusion 224 7.4. Bibliography 224 Chapter 8. Nanolayered Hard Coatings for Mechanical Applications 227 Frédéric SANCHETTE, Cédric DUCROS and Guillaume RAVEL 8.1. Introduction 227 8.2. Towards an ultrahard coating – nanostructuring of transition-elements nitrides obtained by cathodic arc evaporation 230 8.3. Towards a low friction coefficient coating: nanostructuring of carbon- and silicon-based materials elaborated by plasma enhanced chemical vapor deposition 240 8.4. Conclusion 243 8.5. Bibliography 243 Chapter 9. Plating of Nanocomposite Coatings 247 Patrice BERÇOT and Jamal TAKADOUM 9.1. Introduction 247 9.2. Electrolytic co-deposition of metal/particles and modeling 248 9.3. Parameters of the electrolytic composite coatings 254 9.4. Characterization of the composite coatings 260 9.5. Domains of application of the composite coatings 263 9.6. Conclusion 263 9.7. Bibliography 264 Chapter 10. Nanostructured Coatings 271 Guy BARET and Pierre Paul JOBERT 10.1. Introduction 271 10.2. Nanomaterials 272 10.3. Applications 278 10.4. Nanopowders: instructions for use 288 10.5. Economical aspects 290 10.6. Conclusion 291 10.7. Bibliography 291 Chapter 11. Characterization of Coatings: Hardness, Adherence and Internal Stresses 293 Jamal TAKADOUM 11.1. Hardness 293 11.2. Coating adhesion 304 11.3. Residual stresses in coatings 315 11.4. Bibliography 323 Chapter 12. High Temperature Oxidation Resistance of Nanocomposite Coatings 329 David PILLOUD and Jean-François PIERSON 12.1. Introduction 329 12.2. Nanocomposite coating concept 330 12.3. Methods for nanocomposite coating elaboration 331 12.4. Structural characterization 333 12.5. High temperature oxidation behavior 336 12.6. Conclusion 343 12.7. Bibliography 344 List of Authors 349 Index 353

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Book SynopsisBoth naturally-occurring and man-made materials are often heterogeneous materials formed of various constituents with different properties and behaviours. Studies are usually carried out on volumes of materials that contain a large number of heterogeneities. Describing these media by using appropriate mathematical models to describe each constituent turns out to be an intractable problem. Instead they are generally investigated by using an equivalent macroscopic description - relative to the microscopic heterogeneity scale - which describes the overall behaviour of the media. Fundamental questions then arise: Is such an equivalent macroscopic description possible? What is the domain of validity of this macroscopic description? The homogenization technique provides complete and rigorous answers to these questions. This book aims to summarize the homogenization technique and its contribution to engineering sciences. Researchers, graduate students and engineers will find here a unified and concise presentation. The book is divided into four parts whose main topics are Introduction to the homogenization technique for periodic or random media, with emphasis on the physics involved in the mathematical process and the applications to real materials. Heat and mass transfers in porous media Newtonian fluid flow in rigid porous media under different regimes Quasi-statics and dynamics of saturated deformable porous media Each part is illustrated by numerical or analytical applications as well as comparison with the self-consistent approach.Table of ContentsMain notations 17Introduction 21PART ONE. UPSCALING METHODS 27Chapter 1. An Introduction to Upscaling Methods 29Chapter 2. Heterogenous Medium: Is an Equivalent Macroscopic Description Possible? 55Chapter 3. Homogenization by Multiple Scale Asymptotic Expansions 75PART TWO. HEAT AND MASS TRANSFER 107Chapter 4. Heat Transfer in Composite Materials 109Chapter 5. Diffusion/Advection in Porous Media 143Chapter 6. Numerical and Analytical Estimates for the Effective Diffusion Coefficient 161PART THREE. NEWTONIAN FLUID FLOW THROUGH RIGID POROUS MEDIA 195Chapter 7. Incompressible Newtonian Fluid Flow Through a Rigid Porous Medium 197Chapter 8. Compressible Newtonian Fluid Flow Though a Rigid Porous Medium 229Chapter 9. Numerical Estimation of the Permeability of Some Periodic Porous Media 257Chapter 10. Self-consistent Estimates and Bounds for Permeability 275PART FOUR. SATURATED DEFORMABLE POROUS MEDIA 337Chapter 11. Quasi-statics of Saturated Deformable Porous Media 339Chapter 12. Dynamics of Saturated Deformable Porous Media 367Chapter 13. Estimates and Bounds for Effective Poroelastic Coefficients 389Chapter 14. Wave Propagation in Isotropic Saturated Poroelastic Media 407Bibliography . 453Index 473

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Book SynopsisThere are many different vapor phase surface treatments of materials that can be used to produce a wide variety of end results, but each of them are of increasing importance in the pursuit of high performance advanced materials. These techniques differ significantly in the physical or chemical nature of the gas–surface interactions involved, and also in the thickness and morphology of the coatings produced. Applications include advanced semiconductors, optics, and nanotechnology, as well as many more. This book details the most important techniques used in industrial applications, providing coverage from the basic physics to the technical details of each, with emphasis on the macroscopic engineering of the processes and the microscopic characterization of the produced coatings. Vacuum evaporation, cathodic sputtering and ion implantation produce thin films mainly by physical interactions; gas cementation, nitridation, carbonitridation and pack cementation produce thicker surface modifications involving chemical reactions. A section of the book is devoted to chemical vapor deposition (CVD) processes, with dedicated chapters dealing with i) principles and industrial applications, ii) the use of plasma and lasers to assist deposition, and iii) macroscopic modeling of reactors. Alain Galerie has drawn contributions from leading experts at top research universities to produce a complete overview of the vapor phase surface treatments which have an increasing role in modern surface engineering.

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Book SynopsisOver the last 50 years, the methods of investigating dynamic properties have resulted in significant advances. This book explores dynamic testing, the methods used, and the experiments performed, placing a particular emphasis on the context of bounded medium elastodynamics. Dynamic tests have proven to be as efficient as static tests and are often easier to use at lower frequency. The discussion is divided into four parts. Part A focuses on the complements of continuum mechanics. Part B concerns the various types of rod vibrations: extensional, bending, and torsional. Part C is devoted to mechanical and electronic instrumentation, and guidelines for which experimental set-up should be used are given. Part D concentrates on experiments and experimental interpretations of elastic or viscolelastic moduli. In addition, several chapters contain practical examples alongside theoretical discussion to facilitate the readers understanding. The results presented are the culmination of over 30 years of research by the authors and as such will be of great interest to anyone involved in this field.Table of ContentsPreface xxi Acknowledgements xxxi PART I - MECHANICAL AND ELECTRONIC INSTRUMENTATION 1 Chapter 1. Guidelines for Choosing the Experimental Set-up 3 Jean Tuong VINH 1.1. Choice of matrix coefficient to be evaluated and type of wave to be adopted 4 1.2. Influence of frequency range 8 1.3. Dimensions and shape of the samples 9 1.4. Tests at high and low temperature 10 1.5. Sample holder at high temperature 10 1.6. Visual observation inside the ambient room 11 1.7. Complex moduli of viscoelastic materials and damping capacity measurements 11 1.8. Previsional calculation of composite materials 11 1.9. Bibliography 11 Chapter 2. Review of Industrial Analyzers for Material Characterization 13 Jean Tuong VINH 2.1. Rheovibron and its successive versions 14 2.2. Dynamic mechanical analyzer DMA 01dB–Metravib and VHF 104 Metravib analyzer 17 2.3. Bruel and Kjaer complex modulus apparatus (Oberst Apparatus) 18 2.4. Dynamic mechanical analyzer DMA – Dupont de Nemours 980 20 2.5. Elasticimeter using progressive wave PPM 5 22 2.6. Bibliography 24 Chapter 3. Mechanical Part of the Vibration Test Bench 25 Jean Tuong VINH 3.1. Clamping end 25 3.2. Length correction 29 3.3. Supported end 33 3.4. Additional weight or additional torsion lever used as a boundary condition 34 3.5. Free end 34 3.6. Pseudo-clamping sample attachment 35 3.7. Sample suspended by taut threads 38 3.8. Sample on foam rubber plate serving as a mattress 41 3.9. Climatic chamber 41 3.10. Vacuum system 41 3.11. Bibliography 42 Chapter 4. Exciters and Excitation Signals 43 Jean Tuong VINH 4.1. Frequency ranges 43 4.2. Power 43 4.3. Nature and performance of various exciters 44 4.4. Room required for exciter installation 47 4.5. Details for electrodynamic shakers 48 4.6. Low cost electromagnetic exciters with permanent magnet 54 4.7. Piezoelectric and ferroelectric exciters 55 4.8. Design of special ferroelectric transducers 67 4.9. Power piezoelectric exciters 69 4.10. Technical details concerning ultrasonic emitters for the measurement of material stiffness coefficients on ultrasonic test benches 70 4.11. Bibliography 74 4.12. Appendix 4A. Example of ferroelectric plates and disks 74 Chapter 5. Transducers 77 Jean Tuong VINH and Michel NUGUES 5.1. Introduction 77 5.2. Transducers and their principal performance 78 5.3. The main classes of fixed reference transducers 79 5.4. Condenser-type transducer 82 5.5. Inductance transducers 89 5.6. Mutual inductance transducer 92 5.7. Differential transformer transducer 93 5.8. Contactless inductance transducer with a permanent magnet 93 5.9. Eddy current transducer 94 5.10. Seismic transducers 97 5.11. Piezoresistive accelerometer 109 5.12. Other transducers 110 5.13. Force transducers 111 5.14. Bibliography 113 5.15. Appendix 5A. Condenser with polarization 113 5.16. Appendix 5B. Eigenfrequencies of some force transducers: Rayleigh and Rayleigh-Ritz upper bound methods 115 5B.1. Rayleigh’s method 116 5B.2. Rayleigh-Ritz’s method 117 5B.3. Preliminary experimental test on the force transducer 117 Chapter 6. Electronic Instrumentation, Connecting Cautions and Signal Processing 119 Jean Tuong VINH 6.1. Preamplifiers and signal conditioners following the transducers 120 6.2. Cables and wiring considerations 121 6.3. Transducer selection and mountings 123 6.4. Transducer calibration 129 6.5. Digital signal processing systems: an overview 133 6.6. Other signal processing programs 141 6.7. Reasoned choice of excitation signals 142 6.8. Bibliography 146 6.9. Appendix 6A. The Shannon theorem and aliasing phenomenon 147 6.10. Appendix 6B. Time window (or weighting function)150 6B.1. Kaiser-Bessel window 151 6B.2. Hamming window 152 Chapter 7. The Frequency Hilbert Transform and Detection of Hidden Non-linearities in Frequency Responses 155 Jean Tuong VINH 7.1. Introduction 155 7.2. Mathematical expression of the Hilbert transform 157 7.3. Kramer-Kronig’s relationships 162 7.4. Causal signal and Fourier transform 163 7.5. Hilbert transform of a truncated transfer function 164 7.6. Impulse response of a system. Non-causality due to measurement defects 172 7.7. Summary of principal result in sections 7.5 and 7.6 174 7.8. Causalized Hilbert transform 175 7.9. Some practical aspects of Hilbert transform computation 176 7.10. Conclusion 181 7.11. Bibliography 181 7.12. Appendix 7A. Line integral of complex function and Cauchy’s integral 182 7A.1. Analyticity of a function f(z) of complex variable z 182 7A.2. Expression of Cauchy’s integral of the function f(z)/(z- 183 7.13. Appendix 7B. Hilbert transform obtained directly by Guillemin’s method 184 Chapter 8. Measurement of Structural Damping 187 Jean Tuong VINH 8.1. Introduction 187 8.2. Overview of various methods used to evaluate damping ratios in structural dynamics 190 8.3. Measurement of structural damping coefficient by multimodal analysis 197 8.4. The Hilbert envelope time domain method 201 8.5. Detection of hidden non-linearities 203 8.6. How to relate material damping to structural damping? 203 8.7. Concluding remarks 207 8.8. Bibliography 208 PART II - REALIZATION OF EXPERIMENTAL SET-UPS AND INTERPRETATION OF MEASUREMENTS 209 Chapter 9. Torsion Test Benches: Instrumentation and Experimental Results 211 Michel NUGUES 9.1. Introduction 211 9.2. Industrial torsion test bench 211 9.3. Parasitic bending vibration of rod 215 9.4. Shear moduli of transverse isotropic materials 215 9.5. Elastic moduli obtained for various materials 220 9.6. Experimental set-up to obtain dispersion curves in a large frequency range 222 9.7. Experimental results obtained on short samples 224 9.8. Experimental wave dispersion curves obtained by torsional vibrations of a rod with rectangular cross-section 227 9.9. Frequency spectrum for isotropic metallic materials (aluminum and steel alloy) 230 9.10. Impact test on viscoelastic high damping material 232 9.11. Concluding remarks 238 9.12. Bibliography 239 9.13. Appendix 9A. Choice of equations of motion 240 9A.1. Circular cross-section 240 9A.2. Square cross-section 241 9A.3. Rectangular cross-section 241 9A.4. Ratio of Young’s modulus to shear modulus 241 9A.5. Special experimental studies of wave dispersion phenomenon 242 9.14. Appendix 9B. Complementary information concerning formulae used to interpret torsion tests 242 9B.1. Quick overview of Saint Venant’s theory applied to the problem of dynamic Torsion 242 9.15. Appendix 9C. Details concerning the βΤ(c) function in the calculation of rod stiffness CT 245 9.16. Appendix 9D. Compliments concerning the solution of equations of motion with first order theory 246 9D.1. Displacement field 246 9D.2. Relations between two sets of coefficients 246 9D.3. Equations giving the two sets of coefficients Aa, Ba, Ca, Da deduced from the four boundary conditions 248 9D.4. Evaluation of coefficients in [9D.6] 248 9D.5. Equations in Aa, Ba, Ca, Da deduced from the four boundary conditions 249 Chapter 10. Bending Vibration of Rod Instrumentation and Measurements 255 Dominique LE NIZHERY 10.1. Introduction 255 10.2. Realization of an elasticimeter 255 10.3. How to conduct bending tests 262 10.4. Concluding remarks 267 10.5 Bibliography 268 10.6. Appendix 10A. Useful formulae to evaluate the Young’s modulus by bending vibration of rods 268 10A.1. Bernoulli-Euler’s equation 268 10A.2. Timoshenko-Mindlin’s equation 269 10A.3. Boundary conditions and wave number equation 269 10A.4. Important parameters in rod bending vibration 269 10A.5. Expression of the wave number 270 10A.6. Young’s modulus (Bernoulli’s theory) 270 10A.7. Young’s modulus (Timoshenko-Mindlin’s equation) 270 Chapter 11. Longitudinal Vibrations of Rods: Material Characterization and Experimental Dispersion Curves 271 Yvon CHEVALIER and Jean Tuong VINH 11.1. Introduction 271 11.2. Mechanical set-up 272 11.3. Electronic set-up 272 11.4. Estimation of phase velocity 274 11.5. Short samples and eigenvalue calculations for various materials 280 11.6. Experimental results interpreted by the two theories 283 11.7. Influence of slenderness (δL = 2L/h) on eigenfrequency 291 11.8. Experimental results obtained with short rod 292 11.9. Concluding remarks 292 11.10. Bibliography 295 11.11. Appendix 11A. Eigenvalue equation for rod of finite length 296 11.12. Appendix 11B. Additional information concerning solutions of Touratier’s equations 300 11B.1. Eigenequation with elementary theory of motion 301 Chapter 12. Realization of Le Rolland-Sorin’s Double Pendulum and Some Experimental Results 305 Mostefa ARCHI and Jean-Baptiste CASIMIR 12.1. Introduction 305 12.2. Principal mechanical parts of the double pendulum system 305 12.3. Instrumentation 312 12.4. Experimental precautions 315 12.5. Details and characteristics of the elasticimeter 317 12.6. Some experimental results 318 12.7. Damping ratio estimation by logarithmic decrement method 322 12.8. Concluding remarks 324 12.9. Bibliography 325 12.10. Appendix 12A. Equations of motion for the set (pendulums, platform and sample) and Young’s modulus calculation deduced from bending tests 326 12A.1. Equations of motion 326 12A.2. Solutions for pendulum oscillations 328 12A.3. Relationship between beating period τ and sample stiffness k 329 12A.4. Young’s modulus calculation 330 12.11. Appendix 12B. Evaluation of shear modulus by torsion tests 331 12B.1. Energy expression 331 Chapter 13. Stationary and Progressive Waves in Rings and Hollow Cylinders 335 Yvon CHEVALIER and Jean Tuong VINH 13.1. Introduction 335 13.2. Choosing the samples based on material symmetry 336 13.3. Practical realization of a special elasticimeter for curved beams and rings: in plane bending vibrations 337 13.4. Ultrasonic benches 342 13.5. Experimental results and interpretation 343 13.6. List of symbols 358 13.7. Bibliography 359 13.8. Appendix 13A. Evaluation of Young’s modulus by using in plane bending motion of the ring 359 13.9. Appendix 13B. Determination of inertia moment of a solid by means of a three-string pendulum 360 13B.1. Principle of the method 360 13B.2. Calculations 361 13.10. Appendix 13C. Necessary formulae to evaluate Young’s modulus of a straight beam 364 Chapter 14. Ultrasonic Benches: Characterization of Materials by Wave Propagation Techniques 367 Patrick GARCEAU 14.1. Introduction 367 14.2. Ultrasonic transducers 367 14.3. Pulse generator 369 14.4. Mechanical realization of ultrasonic benches 371 14.5. Experimental interpretation of phase velocity and group velocity 375 14.6. Some experimental results on composite materials 380 14.7. Viscoelastic characterization of materials by ultrasonic waves 383 14.8. Bibliography 388 14.9. Appendix 14A. Oblique incidence and energy propagation direction 389 14.10. Appendix 14B. Water immersion bench, measurement of coefficients of stiffness matrix 392 14B.1. Expression of phase velocity in the sample 393 14B.2. Phase velocity measurement by propagation time (?·?nt ) evaluation 394 14B.3. Phase velocity evaluation without time measurements 394 Chapter 15. Wave Dispersion in Rods with a Rectangular Cross-section: Higher Order Theory and Experimentation 397 Maurice TOURATIER 15.1. Introduction 397 15.2. Summary table of some wave dispersion research 398 15.3. Longitudinal wave dispersion: influence of the material and geometry of the bounded medium 399 15.4. Bending wave dispersion 403 15.5. First order for torsional motion in a transverse isotropic rod 408 15.6. Interest in theories with higher degrees of approximation 414 15.7. Experimental set-ups to visualize stationary waves in rods 416 15.8. Electronic set-up and observed signals on a multi-channel oscilloscope 421 15.9. Presentation of experimental results 424 15.10. Concluding remarks 427 15.11. Bibliography 428 15.12. Appendix 15A. Touratier’s theory using Hellinger–Reissner’s mixed fields 429 15A.1. Outline of Touratier’s mixed field theory 429 15A.2. General equations deduced from the two fields principle 432 15A.3. Formulation of the boundary condition problem 432 15A.4. Symmetry considerations concerning the three kinds of motion 433 15A.5. Truncating process for one dimensional theories: extensional waves 437 15A.6. Equations of motion for extensional movement 438 15A.7. Effective front velocity and wave front velocity 439 15A.8. Bending equations of motion 441 15A.9. Equations of motion: torsional vibration 444 15.13. Appendix 15B. Third order Touratier’s theory 445 15B.1. Extensional waves with nine evaluated modes 446 15B.2. Geometrical characteristics of displacement components uj mn and physical interpretation 447 15B.3. Bending mode in the direction x – geometrical interpretation 448 15B.4. Shear motion around longitudinal rod axis 450 List of Authors 453 Index 455

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Book SynopsisIt is well known that solid carbons can be found in various guises with different forms of bulk phases (graphites, diamonds and carbynes) as well as more molecular forms (fullerenes,nanotubes and graphenes) resulting from recent discoveries. The cause of this rich polymorphism is analyzed in the first part of this book (chapters 1-5) with the propensity of carbon atoms for forming different types of homopolar chemical bonds associated with variable coordination numbers. Precursor organic molecules and parent compounds are also described to establish specific links with this rich polymorphism. Then in a second part (chapters 6-10) a comparative review of the main classes of bulk physical properties is presented. This approach emphasizes in particular the electronic behavior of (pi) polyaromatic systems organized in plane and curved atomic sheets. Finally in a third part (chapters 11-15) the surface and interface characteristics are introduced together with the texture and morphology of these multiscale carbon materials. An overview of the main field of applications is related showing the large use and interest for these solids.Table of ContentsIntroduction xiii PART 1. CARBON PHASES, PRECURSORS AND PARENT COMPOUNDS 1 Chapter 1. A Historical Overview 3 1.1. The alchemy of carbon 3 1.2. Elemental carbon and its allotropic varieties 5 1.3. Novel molecular varieties 7 1.4. Natural forms 9 1.5. Contribution from quantum mechanics 14 1.6. Conclusion 21 1.7. Bibliography 21 Chapter 2. Polymorphism of Crystalline Phases 25 2.1. Thermodynamic stability and phase diagram 25 2.2. Classical forms of carbon 37 2.3. Molecular and exotic forms 43 2.4. State of the art and conclusion 53 2.5. Bibliography 54 Chapter 3. Non-Crystalline Carbons 61 3.1. Reminder about defects and imperfections in networks 62 3.2. Thermodynamic approach and the classification of solids 70 3.3. Fabrication and characterization techniques 81 3.4. Conclusion 92 3.5. Bibliography 93 Chapter 4. Derivative Compounds and Analogs 97 4.1. Doping carbons and solid solutions 98 4.2. 2D and 3D analog compounds 111 4.3. Similar materials 116 4.4. Conclusion 118 4.5. Bibliography 118 Chapter 5. From Aromatic Precursors to the Graphene Plane 127 5.1. Condensed polyaromatic systems 128 5.2. The graphene plane 151 5.3. Current situation and conclusion 160 5.4. Bibliography 160 PART 2. PHYSICAL PROPERTIES OF SOLID CARBONS 169 Chapter 6. General Structural Properties 171 6.1. Elastic and mechanic properties 172 6.2. Thermal properties 188 6.3. Conclusion 207 6.4. Bibliography 208 Chapter 7. Electronic Structures and Magnetic Properties 217 7.1. Electronic band structures 218 7.2. Static magnetic properties 227 7.3. Electron spin (or paramagnetic) resonance 240 7.4. NMR 252 7.5. Conclusion 255 7.6. Bibliography 256 Chapter 8. Electronic Transport Properties 265 8.1. Electrical conductivity 270 8.2. Galvanomagnetic properties 293 8.3. Thermoelectric properties 305 8.4. Conclusion 310 8.5. Bibliography 310 Chapter 9. Optical Properties and their Applications 321 9.1. Properties in linear optics 325 9.2. Nonlinear and photo-induced properties 344 9.3. Analysis methods and applications 351 9.4. Conclusion 358 9.5. Bibliography 358 Chapter 10. Vibrational Properties 369 10.1. Phonon spectra in crystalline phases 370 10.2. Specific characteristics of Raman scattering 383 10.3. Data from infrared spectroscopy 394 10.4. Conclusion 399 10.5. Bibliography 400 PART 3. CARBON MATERIALS AND USES 409 Chapter 11. Surface and Interface Phenomena 411 11.1. Physical-chemistry characteristics 412 11.2. Electric and electrochemical aspects 429 11.3. Solid interfaces, tribology and mechano-chemical effects 439 11.4. Conclusion 449 11.5. Bibliography 450 Chapter 12. Chemical Reactivity and Surface Treatment 461 12.1. Oxidation reactions 463 12.2. Hydrogenation and halogenation reactions 480 12.3. Surface treatment and heterogenous catalysis 486 12.4. Conclusion 492 12.5. Bibliography 492 Chapter 13. Divided and Porous Carbons 503 13.1. General presentation of heterogenous carbons 504 13.2. Properties of porous carbons 516 13.3. Competition between chemical reactions and diffusion 533 13.4. Conclusion 540 13.5. Bibliography 541 Chapter 14. Carbon Filaments, Composites and Heterogenous Media 553 14.1. Carbon filaments 554 14.2. Role in composite materials 563 14.3. Random heterogenous media 572 14.4. Conclusion 581 14.5. Bibliography 581 Chapter 15. Use of Carbon Materials 591 15.1. Sensing applications and nanoelectronics 592 15.2. Carbon for energy 596 15.3. Thermostructural composites and transport 610 15.4 Carbons for chemistry and environmental problems 615 15.5. Biocarbons 618 15.6. General conclusion 621 15.7. Bibliography 621 Main Signs and Symbols 631 List of Basic Boxes 634 Index 635

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Book SynopsisNovel techniques for modeling 3D cracks and their evolution in solids are presented. Cracks are modeled in terms of signed distance functions (level sets). Stress, strain and displacement field are determined using the extended finite elements method (X-FEM). Non-linear constitutive behavior for the crack tip region are developed within this framework to account for non-linear effect in crack propagation. Applications for static or dynamics case are provided.Trade Review"The book, intended for the solid mechanics community, is concisely written and includes numerous illustrations." (Booknews, 1 June 2011) Table of ContentsForeword xi Acknowledgements xiii List of Symbols xv Introduction xvii Chapter 1. Elementary Concepts of Fracture Mechanics 1 1.1. Introduction 1 1.2. Superposition principle 3 1.3. Modes of crack straining 4 1.4. Singular fields at cracking point 5 1.5. Crack propagation criteria 10 Chapter 2. Representation of Fixed and Moving Discontinuities 21 2.1. Geometric representation of a crack: a scale problem 22 2.2. Crack representation by level sets 29 2.3. Simulation of the geometric propagation of a crack 52 2.4. Prospects of the geometric representation of cracks 66 Chapter 3. Extended Finite Element Method X-FEM 69 3.1. Introduction 69 3.2. Going back to discretization methods 70 3.3. X-FEM discontinuity modeling 79 3.4. Technical and mathematical aspects 94 3.5. Evaluation of the stress intensity factors 98 Chapter 4. Non-linear Problems, Crack Growth by Fatigue 109 4.1. Introduction 109 4.2. Fatigue and non-linear fracture mechanics 114 4.3. eXtended constitutive law 137 4.4. Applications 164Chapter 5. Applications: Numerical Simulation of Crack Growth 173 5.1. Energy conservation: an essential ingredient 173 5.2. Examples of crack growth by fatigue simulations 182 5.3. Dynamic fracture simulation 192 5.4. Simulation of ductile fracture 207 Conclusions and Open Problems 227 Summary 233 Bibliography 235 Index 253

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Book SynopsisWall turbulence is encountered in many technological applications as well as in the atmosphere, and a detailed understanding leading to its management would have considerable beneficial consequences in many areas. A lot of inspired work by experimenters, theoreticians, engineers and mathematicians has been accomplished over recent decades on this important topic and Statistical Approach to Wall Turbulence provides an updated and integrated view on the progress made in this area. Wall turbulence is a complex phenomenon that has several industrial applications, such as in aerodynamics, turbomachinery, geophysical flows, internal engines, etc. Several books exist on fluid turbulence, but Statistical Approach to Wall Turbulence is original in the sense that it focuses solely on the turbulent flows bounded by solid boundaries. The book covers the different physical aspects of wall turbulence, beginning with classical phenomenological aspects before advancing to recent research in the effects of the Reynolds numbers, near wall coherent structures, and wall turbulent transport process. This book would be of interest to postgraduate and undergraduate students in mechanical, chemical, and aerospace engineering, as well as researchers in aerodynamics, combustion, and all applications of wall turbulence.Table of ContentsForeword ix Ivan MARUSIC Introduction xi Chapter 1. Basic Concepts 1 1.1. Introduction 1 1.2. Fundamental equations 1 1.3. Notation 4 1.4. Reynolds averaged Navier-Stokes equations 4 1.5. Basic concepts of turbulent transport mechanisms 6 1.6. Correlation tensor dynamics 11 1.7. Homogeneous turbulence 15 1.8. Isotropic homogeneous turbulence 20 1.9. Axisymmetric homogeneous turbulence 33 1.10. Turbulence scales 35 1.11. Taylor hypothesis 39 1.12. Approaches to modeling wall turbulence 40 Chapter 2. Preliminary Concepts: Phenomenology, Closures and Fine Structure 45 2.1. Introduction 45 2.2. Hydrodynamic stability and origins of wall turbulence 46 2.3. Reynolds equations in internal turbulent flows 55 2.4. Scales in turbulent wall flow 55 2.5. Eddy viscosity closures 56 2.6. Exact equations for fully developed channel flow 61 2.7. Algebraic closures for the mixing length in internal flows 65 2.8. Some illustrations using direct numerical simulations at low Reynolds numbers 69 2.9. Transition to turbulence in a boundary layer on a flat plate 76 2.10. Equations for the turbulent boundary layer 77 2.11. Mean vorticity 81 2.12. Integral equations 83 2.13. Scales in a turbulent boundary layer 85 2.14. Power law distributions and simplified integral approach 85 2.15. Outer layer 88 2.16. Izakson-Millikan-von Mises overlap 89 2.17. Integral quantities 91 2.18. Wake region 94 2.19. Drag coefficient in external turbulent flows 96 2.20. Asymptotic behavior close to the wall 98 2.21. Coherent wall structures – a brief introduction 101 Chapter 3. Inner and Outer Scales: Spectral Behavior 105 3.1. Introduction105 3.2. Townsend-Perry analysis in the fully-developed turbulent sublayer 107 3.3. Spectral densities 110 3.4. Clues to the 1x k _ behavior, and discussion 124 3.5. Spectral density vv E and cospectral density uv E 129 3.6. Two-dimensional spectral densities 131 Chapter 4. Reynolds Number-Based Effects 137 4.1. Introduction 137 4.2. The von Karman constant and the renormalization group 140 4.3. Complete and incomplete similarity 146 4.4. Symmetries and their consequences 155 4.5. Principle of asymptotic invariance. Approach of W.K. George 163 4.6. Mean velocity distribution. Summary 185 4.7. Townsend’s attached eddies 185 4.8. Overlap region in internal flows 228 4.9. Two-point correlations 230 4.10. Active and passive Townsend eddies 239 4.11. Fine structure 249 Chapter 5. Vorticity 259 5.1. Introduction 259 5.2. General characteristics of vorticity 259 5.3. Reynolds shear stress and vorticity transport 261 5.4. Characteristics of the vorticity field close to a wall 264 5.5. Statistics and fine structure 270 5.6. Vorticity transport 277 5.7. Estimating the importance of non-linearity close to the wall 284 5.8. Measurements 287 Notations Used 291 Subscripts and superscripts 293 Greek letters 294 Abbreviations 295 Bibliography 297 Index 309

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Book SynopsisThe design of mechanical structures with improved and predictable durability cannot be achieved without a thorough understanding of the mechanisms of fatigue damage and more specifically the relationships between the microstructure of materials and their fatigue properties. Written by leading experts in the field, this book (which is complementary to Fatigue of Materials and Structures: Application to Damage and Design, also edited by Claude Bathias and André Pineau), provides an authoritative, comprehensive and unified treatment of the mechanics and micromechanisms of fatigue in metals, polymers and composites. Each chapter is devoted to one of the major classes of materials or to different types of fatigue damage, thereby providing overall coverage of the field. The book deals with crack initiation, crack growth, low-cycle fatigue, gigacycle fatigue, shorts cracks, fatigue micromechanisms and the local approach to fatigue damage, corrosion fatigue, environmental effects and variable amplitude loadings, and will be an important and much used reference for students, practicing engineers and researchers studying fracture and fatigue in numerous areas of mechanical, structural, civil, design, nuclear, and aerospace engineering as well as materials science.Table of ContentsForeword xi Stephen D. ANTOLOVICH Chapter 1. High Temperature Fatigue 1 Stephen D. ANTOLOVICH and Andre PINEAU 1.1. Introduction and overview 1 1.2. 9 to 12% Cr steels 7 1.3. Austenitic stainless steels 22 1.4. Fatigue of superalloys 40 1.5. Lifespan prediction in high-temperature fatigue 104 1.6. Conclusions 114 1.7. Acknowledgments 118 1.8. Bibliography 118 Chapter 2. Analysis of Elasto-plastic Strains and Stresses Near Notches Subjected to Monotonic and Cyclic Multiaxial Loading Paths 131 Gregory GLINKA 2.1. Introduction 131 2.2. Multiaxial fatigue parameters 134 2.3. Elasto-plastic notch-tip stress-strain calculation methods 146 2.4. Comparison of notch stress-strain calculations with numerical data 164 2.5. Conclusion 173 2.6. Bibliography 173 2.7. Symbols 176 Chapter 3. Fatigue of Composite Materials 179 Claude BATHIAS 3.1. Introduction 179 3.2. Drastic differences between the fatigue of composites and metals 183 3.3. Notch effect on fatigue strength 191 3.4. Effect of a stress on composite fatigue 193 3.5. Fatigue after impact 198 3.6. Fatigue damage criteria 199 3.7. Conclusion 202 3.8. Bibliography 203 Chapter 4. Fatigue of Polymers and Elastomers 205 Claude BATHIAS 4.1. Introduction 205 4.2. Life of polymers 206 4.3. Crack propagation within polymers 207 4.4. Damaging mechanisms of polymers 208 4.5. Specific case of the fatigue of elastomers 210 4.6. The life of natural rubbers 211 4.7. Crack propagation in natural rubber 213 4.8. Propagation mechanisms of cracks in natural rubber 217 4.9. Multiaxial fatigue of rubbers 219 4.10. Cavitation of rubbers 221 4.11. Conclusion 222 4.12. Bibliography 222 Chapter 5. Probabilistic Design of Structures Submitted to Fatigue 223 Bruno SUDRET 5.1. Introduction 223 5.2. Treatment of hazard in mechanical models 224 5.3. Plotting probabilistic S–N curves 229 5.4. Probabilistic design with respect to crack initiation 237 5.5. Probabilistic propagation models 245 5.6. Conclusion 252 5.7. Appendix A: probability theory reminder 253 5.8. Bibliography 259 Chapter 6. Prediction of Fatigue Crack Growth within Structures 265 Jean LEMAITRE 6.1. Prediction problems 265 6.2. Crack growth laws 268 6.3. Calculation of cracking variables 282 6.4. Resolution method of the cracking equations 289 6.5. New directions 296 6.6. Bibliography 296 List of Authors 299 Index 301

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Book SynopsisSelf-Compacting Concrete (SCC) is a relatively new building material. Nowadays, its use is progressively changing the method of concrete placement on building sites. However, the successful use of SCC requires a good understanding of the behavior of this material, which is vastly different from traditional concrete. For this purpose, a lot of research has been conducted on this area all over the world since 10 years. Intended for both practitioners and scientists, this book provides research results from the rheological behavior of fresh concrete to durability.Trade Review"This book provides research findings ranging from the rheological behaviour of fresh concrete to the durability of SSC." (Detail, 1 January 2012)Table of ContentsIntroduction ix Chapter 1. Design, Rheology and Casting of Self-Compacting Concretes 1 Sofiane AMZIANE, Christophe LANOS and Michel MOURET 1.1. Towards a fluid concrete 1 1.2. SCC formulation basics 7 1.3. SCC rheology 20 1.4. Industrial practices 42 1.5. Forces exerted by SCCs on formworks 50 1.6. Bibliography 59 Chapter 2. Early Age Behavior 67 Philippe TURCRY and Ahmed LOUKILI 2.1. Introduction 67 2.2. Hydration and its consequences 68 2.3. Early age desiccation and its consequences: different approaches to the problem 70 2.4. Plastic shrinkage and drop in capillary pressure 74 2.5. Comparison of plastic shrinkage for SCCs and conventional concretes 79 2.6. Influence of composition on free plastic shrinkage 86 2.7. Cracking due to early drying 89 2.8. Summary 93 2.9. Bibliography 95 Chapter 3. Mechanical Properties and Delayed Deformations 99 Thierry VIDAL, Philippe TURCRY, Stéphanie STAQUET and Ahmed LOUKILI 3.1. Introduction 99 3.2. Instantaneous mechanical properties 100 3.3. Differences in mechanical behavior 110 3.4. Behavior of steel-concrete bonding 122 3.5. Bibliography 130 Chapter 4. Durability of Self-Compacting Concrete 141 Emmanuel ROZIÈRE and Abdelhafid KHELIDJ 4.1. Introduction 141 4.2. Properties and parameters that influence durability 143 4.3. Transport phenomena 152 4.4. Degradation mechanisms 159 4.5. Conclusion 202 4.6. Bibliography 203 Chapter 5. High Temperature Behavior of Self-Compacting Concretes 215 Hana FARES, Sébastien RÉMOND, Albert NOUMOWÉ and Geert DE SCHUTTER 5.1. Introduction 215 5.2. Changes in SCC microstructure and physico-chemical properties with temperature 216 5.3. Mechanical behavior of SCCs at high temperature 240 5.4. Thermal stability 247 5.5. Conclusion 252 5.6. Bibliography 253 Glossary 259 List of Authors 261 Index 263

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Book SynopsisThis book presents recent advances related to the following two topics: how mechanical fields close to material or geometrical singularities such as cracks can be determined; how failure criteria can be established according to the singularity degrees related to these discontinuities. Concerning the determination of mechanical fields close to a crack tip, the first part of the book presents most of the traditional methods in order to classify them into two major categories. The first is based on the stress field, such as the Airy function, and the second resolves the problem from functions related to displacement fields. Following this, a new method based on the Hamiltonian system is presented in great detail. Local and energetic approaches to fracture are used in order to determine the fracture parameters such as stress intensity factor and energy release rate. The second part of the book describes methodologies to establish the critical fracture loads and the crack growth criteria. Singular fields for homogeneous and non-homogeneous problems near crack tips, v-notches, interfaces, etc. associated with the crack initiation and propagation laws in elastic and elastic-plastic media, allow us to determine the basis of failure criteria. Each phenomenon studied is dealt with according to its conceptual and theoretical modeling, to its use in the criteria of fracture resistance; and finally to its implementation in terms of feasibility and numerical application. Contents 1. Introduction.Part 1: Stress Field Analysis Close to the Crack Tip2. Review of Continuum Mechanics and the Behavior Laws.3. Overview of Fracture Mechanics.4. Fracture Mechanics.5. Introduction to the Finite Element Analysis of Cracked Structures.Part 2: Crack Growth Criteria6. Crack Propagation.7. Crack Growth Prediction in Elements of Steel Structures Submitted to Fatigue.8. Potential Use of Crack Propagation Laws in Fatigue Life Design.Table of ContentsPreamble xiii Preface xv Notations xix Chapter 1 1 PART 1: STRESS FIELD ANALYSIS CLOSE TO THE CRACK TIP 5 Chapter 2. Review of Continuum Mechanics and the Behavior Laws 7 2.1. Kinematic equations 9 2.2. Equilibrium equations in a volume element 16 2.3. Behavior laws 20 2.4. Energy formalism 50 2.5. Solution of systems of equations of continuum mechanics and constitutive behavior law 63 2.6. Review of the finite element solution 72 Chapter 3. Overview of Fracture Mechanics 81 3.1. Fracture process 83 3.2. Basic modes of fracture 84 Chapter 4. Fracture Mechanics. 87 4.1. Determination of stress, strain and displacement fields around a crack in a homogeneous, isotropic and linearly elastic medium 90 4.2. Plastic analysis around a crack in an isotropic homogeneous medium 144 4.3. Case of a heterogeneous medium: elastic multimaterials 164 4.4. New modeling approach to singular fracture fields 165 Chapter 5. Introduction to the Finite Element Analysis of Cracked Structures 187 5.1. Modeling of a singular field close to the crack tip 188 5.2. Energetic methods 200 5.3. Nonlinear behavior 208 5.4. Specific finite elements for the calculation of cracked structures 213 5.5. Study of a finite elements program in a 2D linear elastic medium. 216 5.6. Application to the calculation of the J-integral in mixed mode 224 5.7. Different meshing fracture monitoring techniques by finite elements 229 PART 2: CRACK GROWTH CRITERIA 235 Chapter 6. Crack Propagation 237 6.1. Brittle fracture 239 6.2. Crack extension 265 6.3. Crack extension criterion in an elastic plastic medium 272 6.4. Crack-extension criterion from V-notches 275 6.5. Fracture following crack growth under high-cycle number fatigue 277 6.6. Crack propagation laws 279 6.7. Approaches used for the calculation of fatigue lifetime 286 6.8. Case of the variable amplitude loading 296 6.9. Crack retardation effect due to overloading 312 6.10. “Reliability–failure” in the presence of random variables 318 Chapter 7. Crack Growth Prediction in Elements of Steel Structures Submitted to Fatigue 331 7.1. Significance and analysis by calculation of stresses around the local effect 333 7.2. Crack initiation under fatigue 343 7.3. Localization and sensitivity to rupture of cracks 367 7.4. Extension of the initiated crack under fatigue 375 Chapter 8. Potential Use of Crack Propagation Laws in Fatigue Life Design 395 8.1. Calculation of the crack propagation fatigue life of a welded-joint 395 8.2. Study of the influence of different parameters on fatigue life 402 8.3. Statistical characterization of the initial crack size according to the welding procedure 404 8.4. Initiation/propagation coupled models: two phase models 410 8.5. Development of a damage model taking into account the crack growth phenomenon 419 8.6. Taking into account the presence of residual welding stresses on crack propagation 423 8.7. Consideration of initial crack length under variable amplitude loading 430 8.8. Propagation of short cracks in the presence of a stress gradient 433 8.9. Probabilistic approach to crack propagation fatigue life: reliability–failure 440 Conclusion 451 Bibliography 455 Index 477

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Book SynopsisThe main purpose of this book is to put forward the fundamental role of grain boundaries in the plasticity of crystalline materials. To understand this role requires a multi-scale approach to plasticity: starting from the atomic description of a grain boundary and its defects, moving on to the elemental interaction processes between dislocations and grain boundaries, and finally showing how the microscopic phenomena influence the macroscopic behaviors and constitutive laws. It involves bringing together physical, chemical and mechanical studies. The investigated properties are: deformation at low and high temperature, creep, fatigue and rupture.Table of ContentsPreface xi Chapter 1. Grain Boundary Structures and Defects 1 Jany THIBAULT-PENISSON and Louisette PRIESTER 1.1. Equilibrium structure of grain boundaries 1 1.2. Crystalline defects of grain boundaries 18 1.3. Conclusion 41 1.4. Bibliography 42 Chapter 2. Elementary Grain Boundary Deformation Mechanisms 47 Jean-Philippe COUZINIE and Louisette PRIESTER 2.1. Dislocation in close proximity to a grain boundary 48 2.2. Elastic interaction between dislocations and grain boundaries: image force 49 2.3. Short range (or core) interaction between dislocations and grain boundaries 52 2.4. Relaxation of stress fields associated with extrinsic dislocations 81 2.5. Relationships between elementary interface mechanisms and mechanical behaviors of materials 98 2.6. Bibliography 102 Chapter 3. Grain Boundaries in Cold Deformation 109 Colette REY, Denis SOLAS and Olivier FANDEUR 3.1. Introduction 109 3.2. Plastic compatibility and incompatibility of deformation at grain boundaries 111 3.3. Internal stresses in polycrystal grains 117 3.4. Modeling local mechanical fields using the finite element method (FEM)129 3.5. Hall-Petch’s law, geometrically necessary dislocations 139 3.6. Sub-grain boundaries and grain boundaries in deformation and recrystallization 145 3.7. Conclusion 155 3.8. Bibliography 156 Chapter 4. Creep and High Temperature Plasticity: Grain Boundary Dynamics 165 Sylvie LARTIGUE-KORINEK and Claude Paul CARRY 4.1. Introduction 165 4.2. Grain boundaries and grain growth 168 4.3. Grain boundaries and creep: mechanisms and phenomenological laws 174 4.4. Grain boundaries and superplasticity 197 4.5. Prospects: creep of nanograined materials 208 4.6. Bibliography 209 Chapter 5. Intergranular Fatigue 217 André PINEAU and Stephen ANTOLOVICH 5.1. Introduction 217 5.2. Low temperature intergranular fatigue 221 5.3. High temperature fatigue 252 5.4. Conclusion 271 5.5. Acknowledgements 272 5.6. Bibliography 272 Chapter 6. Intergranular Segregation and Crystalline Material Fracture 281 Anna FRACZKIEWICZ and Krzysztof WOLSKI 6.1. Grain boundaries and fracture 282 6.2. Intergranular segregation 286 6.3. Segregation and intergranular fracture 297 6.4. Intergranular fracture induced by liquid metals 308 6.5. General conclusion 320 6.6. Bibliography 321 APPENDICES 327 Appendix 1. Bicrystallography and Topological Characterization of Interfacial Defects 329 Sylvie LARTIGUE-KORINEK and Louisette PRIESTER Appendix 2. Appendices of Chapter 3 333 Colette REY, Denis SOLAS and Olivier FANDEUR List of Authors 341 Index 343

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Book SynopsisThis book addresses artificial materials including photonic crystals (PC) and metamaterials (MM). The first part is devoted to design concepts: negative permeability and permittivity for negative refraction, periodic structures, transformation optics. The second part concerns PC and MM in stop band regime: from cavities, guides to high impedance surfaces. Abnormal refraction, less than one and negative, in PC and MM are studied in a third part, addressing super-focusing and cloaking. Applications for telecommunications, lasers and imaging systems are also explored.Table of ContentsIntroduction xi PART 1. A FEW FUNDAMENTAL CONCEPTS 1 Chapter 1. Definitions and Concepts 3 1.1. Effective parameters of materials 3 1.2. Terminology of artificial materials 6 1.3. Negative refraction: stakes and consequences 8 1.4. Bibliography 11 Chapter 2. The Metamaterial Approach – Permeability and Permittivity Engineering 13 2.1. Background history 13 2.2. An imbricated lattice approach 17 2.3. Cell approach 23 2.4. Alternative approach: Mie resonances 31 2.5. Bibliography 33 Chapter 3. Photonic Crystal Approach – Band Gap Engineering 37 3.1. Historical background 37 3.2. Study tool: band structure 39 3.3. 2D ½ photonic crystals 44 3.4. A few words on three-dimensional photonic crystals 53 3.5. Conclusion: metamaterials or photonic crystals? 55 3.6. Bibliography 56 Chapter 4. Transformation Optics 59 4.1. Context 59 4.2. Method description 60 4.3. Bibliography 69 PART 2. MATERIALS USED IN A BAND GAP REGIME 71 Chapter 5. Point and Extended Defects in Photonic Crystals 73 5.1. Context 73 5.2. Defect zoology 74 5.3. Selectivity of photonic crystal microcavities 77 5.4. Waveguiding in photonic crystals 82 5.5. Slowing down light 90 5.6. Bibliography 92 Chapter 6. Routing Devices made from Photonic Crystals 95 6.1. The building brick: the add/drop filter 95 6.2. A few photonic crystal approaches 98 6.3. Interference-based couplers 100 6.4. Conclusion 117 6.5. Bibliography 117 Chapter 7. Single Negative Metamaterials 121 7.1. Context 121 7.2. ENGs: negative permittivity materials 122 7.3. MNGs: negative permeability materials 128 7.4. What of frequency-selective surfaces? 132 7.5. Bibliographyc 135 PART 3. MATERIALS IN AN ABNORMAL REFRACTION REGIME (N < 1 AND N < 0) 137 Chapter 8. Two-dimensional Microwave Balanced Composite Prism 139 8.1. Why use a microwave prism? 139 8.2. Conception and sizing of a balanced composite lattice 140 8.3. Two-dimensional prism 147 8.4. Bibliography 154 Chapter 9. Metal-dielectric Materials – from the Terahertz to the Visible 157 9.1. From the terahertz to the infrared 157 9.2. A backward propagation line at terahertz frequency 158 9.3. From “nano”-resonators to “fishnets” 163 9.4. Three-dimensional metamaterials 172 9.5. Bibliography 174 Chapter 10. Abnormal Refraction in Photonic Crystals 177 10.1. Context 177 10.2. (An)isotropy in photonic crystals 178 10.3. Exploiting anisotropy 185 10.4. Focalization and negative refraction: looking for isotropy 189 10.5. Bibliography 194 Chapter 11. A Photonic Crystal Flat Lens at Optical Wavelength 197 11.1. A bit of background 197 11.2. How to define a typical prototype at optical wavelengths 198 11.3. Lens optimization: impedance and resolution 201 11.4. Experiments 213 11.5. Reverse engineering: from a two-dimensional prototype to three-dimensional reality 218 11.6. Conclusion 221 11.7. Bibliography 222 Chapter 12. Wave-controlling Systems – Towards Bypass and Invisibility 225 12.1. “Transformation optics” or “dispersion engineering” 225 12.2. Component approaches for controlling waves 226 12.3. Invisibility at terahertz frequencies: Mie resonances 241 12.4. An alternative with the photonic crystal: the butterfly 246 12.5. Perspectives 250 12.6. Bibliography 250 PART 4. MOVING TOWARD APPLICATIONS 253 Chapter 13. Guiding, Filtering and Routing Electromagnetic Waves 255 13.1. Context 255 13.2. Guiding: propagation lines and tunable phase shifters 256 13.3. Filtering 266 13.4. Metamaterial-based routing 273 13.5. Conclusion 276 13.6. Bibliography 276 Chapter 14. Antennas 279 14.1. Towards the miniaturization of transmission/reception systems 279 14.2. Directivity engineering 280 14.3. Subwavelength sizing 293 14.4. Conclusion 298 14.5. Bibliography 299 Chapter 15. Optics: Fibers and Cavities 301 15.1. Optical issues: the privileged domain of photonic crystals 301 15.2. Microstructured optical fibers 302 15.3. Toward zero threshold lasers 310 15.4. Bibliography 318 Chapter 16. Detection, Imaging and Tomography Systems 321 16.1. From detection to imaging 321 16.2. Terahertz sensors 322 16.3. Direct approach for imaging 326 16.4. Detection and image reconstruction 328 16.5. A vast field to explore 337 16.6. Bibliography 339 Conclusion 341 Index 345

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Book SynopsisThe book, prepared in honor of the retirement of Professor J. Mazars, provides a wide overview of continuum damage modeling applied to cementitious materials. It starts from micro-nanoscale analyses, then follows on to continuum approaches and computational issues. The final part of the book presents industry-based case studies. The contents emphasize multiscale and coupled approaches toward the serviceability and the safety of concrete structures.Table of ContentsPreface xi Gilles PIJAUDIER-CABOT and Frédéric DUFOUR Chapter 1. Bottom–Up: From Atoms to Concrete Structures 1 Franz-Josef ULM and Roland J-M PELLENQ 1.1. Introduction 1 1.2. A realistic molecular model for calcium-silicatehydrates 2 1.3. Probing C-S-H microtexture by nanoindentation 9 1.4. Conclusions 15 1.5. Bibliography 16 Chapter 2. Poromechanics of Saturated Isotropic Nanoporous Materials 19 Romain VERMOREL, Gilles PIJAUDIER-CABOT,Christelle MIQUEU and Bruno MENDIBOURE 2.1. Introduction 20 2.2. Results from molecular simulations 22 2.3. Poromechanical model 24 2.4. Adsorption-induced swelling and permeability change in nanoporous materials 37 2.5. Discussion – interaction energy and entropy 42 2.6. Conclusions 46 2.7. Acknowledgments 47 2.8. Bibliography 48 Chapter 3. Stress-based Non-local Damage Model 51 Cédric GIRY and Frédéric DUFOUR 3.1. Introduction 52 3.2. Non-local damage models 57 3.3. Initiation of failure 67 3.4. Bar under traction 70 3.5. Description of the cracking evolution in a 3PBT of a concrete notched beam 79 3.6. Conclusions 82 3.7. Acknowledgments 84 3.8. Bibliography 84 Chapter 4. Discretization of Higher Order Gradient Damage Models Using Isogeometric Finite Elements 89 Clemens V. VERHOOSEL, Michael A. SCOTT, Michael J. BORDEN, Thomas J.R. HUGHES and René DE BORST 4.1. Introduction 89 4.2. Isotropic damage formulation 91 4.3. Isogeometric finite elements 97 4.4. Numerical simulations 103 4.5. Conclusions 115 4.6. Acknowledgments 116 4.7. Bibliography 116 Chapter 5. Macro and Mesoscale Models to Predict Concrete Failure and Size Effects 121 David GRÉGOIRE, Peter GRASSL, Laura B. ROJAS-SOLANO and Gilles PIJAUDIER-CABOT 5.1. Introduction 122 5.2. Experimental procedure 125 5.3. Numerical simulations 134 5.4. Conclusions 152 5.5. Acknowledgments 153 5.6. Bibliography 153 Chapter 6. Statistical Aspects of Quasi-Brittle Size Effect and Lifetime, with Consequences for Safety and Durability of Large Structures 161 Zdenìk P. BA?ANT, Jia-Liang LE and Qiang YU 6.1. Introduction 161 6.2. Type-I size effect derived from atomistic fracture mechanics 164 6.3. Size effect on structural lifetime 170 6.4. Consequences of ignoring Type-2 size effect 172 6.5. Conclusion 177 6.6. Acknowledgments 177 6.7. Bibliography 178 Chapter 7. Tertiary Creep: A Coupling Between Creep and Damage – Application to the Case of Radioactive Waste Disposal 183 J.M. TORRENTI, T. DE LARRARD and F. BENBOUDJEMA 7.1. Introduction to tertiary creep 184 7.2. Modeling of tertiary creep using a damage model coupled to creep 185 7.3. Comparison with experimental results 189 7.4. Application to the case of nuclear waste disposal 190 7.5. Conclusions 197 7.6. Bibliography 198 Chapter 8. Study of Damages and Risks Related to Complex Industrial Facilities 203 Bruno GÉRARD, Bruno CAPRA, Gaël THILLARD and Christophe BAILLIS 8.1. Context 203 8.2. Introduction to risk management 204 8.3. Case study: computation process 206 8.4. Application 212 8.5. Conclusion 219 8.6. Acknowledgment 220 8.7. Bibliography 220 Chapter 9. Measuring Earthquake Damages to a High Strength Concrete Structure 221 Patrick PAULTRE, Benedikt WEBER, Sébastian MOUSSEAU and Jean PROULX 9.1. Introduction 221 9.2. Overview of the selected testing methods 222 9.3. Two-storey HPC building 223 9.4. Inducing damage – pseudo-dynamic testing procedures 227 9.5. Evaluating damage – forced vibration testing procedures 236 9.6. Damage detection – analytical evaluation 239 9.7. Summary and conclusions 248 9.8. Bibliography 249 List of Authors 251 Index 253

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Book SynopsisThis book presents reviews of various aspects of radiation/matter interactions, be these instrumental developments, the application of the study of the interaction of X-rays and materials to a particular scientific field, or specific methodological approaches. The overall aim of the book is to provide reference summaries for a range of specific subject areas within a pedagogical framework. Each chapter is written by an author who is well known within their field and who has delivered an invited lecture on their subject area as part of the “RX2009 – X-rays and Materials” colloquium that took place in December 2009 at Orsay in France. The book consists of five chapters on the subject of X-ray diffraction, scattering and absorption. Chapter 1 gives a detailed presentation of the capabilities and potential of beam lines dedicated to condensed matter studies at the SOLEIL synchrotron radiation source. Chapter 2 focuses on the study of nanoparticles using small-angle X-ray scattering. Chapter 3 discusses the quantitative studies of this scattering signal used to analyze these characteristics in detail. Chapter 4 discusses relaxor materials, which are ceramics with a particularly complex microstructure. Chapter 5 discusses an approach enabling the in situ analysis of these phase transitions and their associated microstructural changes.Table of ContentsPreface xi Chapter 1. Synchrotron Radiation: Instrumentation in Condensed Matter 1 Jean-Paul ITIE, François BAUDELET, Valérie BRIOIS, Eric ELKAÏM, Amor NADJI and Dominique THIAUDIÈRE 1.1. Introduction 1 1.2. Light sources in the storage ring 2 1.3. Emittance and brilliance of a source 6 1.4. X-ray diffraction with synchrotron radiation 8 1.5. X-ray absorption spectroscopy usingsynchrotron radiation 13 1.6. SAMBA: the X-ray absorption spectroscopy beam line of SOLEIL for 4–40 keV 20 1.7. The DIFFABS beam line 27 1.8. CRISTAL beam line 34 1.9. The SOLEIL ODE line for dispersive EXAFS 38 1.10. Conclusion 43 1.11. Bibliography 44 Chapter 2. Nanoparticle Characterization using Central X-ray Diffraction 49 Olivier SPALLA 2.1. Introduction 49 2.2. Definition of scattered intensity 50 2.3. Invariance principle 52 2.4. Behavior for large q: the Porod regime 55 2.5. Particle-based systems 59 2.6. An absolute scale for measuring particle numbers 75 2.7. Conclusion 78 2.8. Bibliography 79 Chapter 3. X-ray Diffraction for Structural Studies of Carbon Nanotubes and their Insertion Compounds 81 Julien CAMBEDOUZOU and Pascale LAUNOIS 3.1. Introduction 81 3.2. Single-walled carbon nanotubes 85 3.3. Multi-walled carbon nanotubes 96 3.4. Hybrid nanotubes 102 3.5. Textured powder samples 110 3.6. Conclusion 121 3.7. Bibliography 122 Chapter 4. Dielectric Relaxation and Morphotropic Phases in Nanomaterials 129 Jean-Michel KIAT 4.1. Introduction 129 4.2. Dielectric relaxation and morphotropic region: definition and mechanism 130 4.3. Relaxation, morphotropic region and size reduction 163 4.4. Conclusion 174 4.5. Acknowledgements 175 4.6. Bibliography 175 Chapter 5. Evolution of Solid-state Microstructures in Polycrystalline Materials: Application of High-energy X-ray Diffraction to Kinetic and Phase Evolution Studies 181 Elisabeth AEBY-GAUTIER, Guillaume GEANDIER, Moukrane DEHMAS, Fabien BRUNESEAUX, Adeline BENETEAU, Patrick WEISBECKER, Benoît APPOLAIRE and Sabine DENIS 5.1. Introduction 181 5.2. Experimental methods 183 5.3. Results 195 5.4. Conclusion 213 5.5. Acknowledgements 214 5.6. Bibliography 214 List of Authors 221 Index 223

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Book SynopsisThe aim of this book is to summarize the current most effective methods for modeling, simulating, and optimizing metal forming processes, and to present the main features of new, innovative methods currently being developed which will no doubt be the industrial tools of tomorrow. It discusses damage (or defect) prediction in virtual metal forming, using advanced multiphysical and multiscale fully coupled constitutive equations. Theoretical formulation, numerical aspects as well as application to various sheet and bulk metal forming are presented in detail.Virtual metal forming is nowadays inescapable when looking to optimize numerically various metal forming processes in order to design advanced mechanical components. To do this, highly predictive constitutive equations accounting for the full coupling between various physical phenomena at various scales under large deformation including the ductile damage occurrence are required. In addition, fully 3D adaptive numerical methods related to time and space discretization are required in order to solve accurately the associated initial and boundary value problems. This book focuses on these two main and complementary aspects with application to a wide range of metal forming and machining processes. Contents 1. Elements of Continuum Mechanics and Thermodynamics.2. Thermomechanically-Consistent Modeling of the Metals Behavior with Ductile Damage.3. Numerical Methods for Solving Metal Forming Problems.4. Application to Virtual Metal Forming.Table of ContentsPreface xiii Principle of Mathematical Notations xix Chapter 1. Elements of Continuum Mechanics and Thermodynamics 1 1.1. Elements of kinematics and dynamics of materially simple continua 2 1.2. On the conservation laws for the materially simple continua. 33 1.3. Materially simple continuum thermodynamics and the necessity of constitutive equations 39 1.4. Mechanics of generalized continua. Micromorphic theory 55 Chapter 2. Thermomechanically-Consistent Modeling of the Metals Behavior with Ductile Damage 63 2.1. On the main schemes for modeling the behavior of materially simple continuous media 64 2.2. Behavior and fracture of metals and alloys: some physical and phenomenological aspects 69 2.3. Theoretical framework of modeling and main hypotheses 91 2.4. State potential: state relations 113 2.5. Dissipation analysis: evolution equations 139 2.6. Modeling of the damage-induced volume variation 194 2.7. Modeling of the contact and friction between deformable solids 200 2.8. Nonlocal modeling of damageable behavior of micromorphic continua 215 2.9. On the micro–macro modeling of inelastic flow with ductile damage 226 Chapter 3. Numerical Methods for Solving Metal Forming Problems 243 3.1. Initial and boundary value problem associated with virtual metal forming processes 244 3.2. Temporal and spatial discretization of the IBVP 259 3.3. On some global resolution scheme of the IBVP 270 3.4. Local integration scheme: state variables computation 304 3.5. Adaptive analysis of damageable elasto-inelastic structures 337 3.6. On other spatial discretization methods 347 Chapter 4. Application to Virtual Metal Forming 355 4.1. Why use virtual metal forming? 356 4.2. Model identification methodology 359 4.3. Some applications 431 4.4. Toward the optimization of forming and machining processes 484 Appendix: Legendre–Fenchel Transformation 493 Bibliography 499 Index 515

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Book SynopsisRecent advances into the wear of advanced materials In general, wear is currently defined as “the progressive loss of material from the operating surface of a body occurring as a result of relative motion at the surface”. It is related to surface interactions and more specifically to the form of contact due to relative motion. Wear is rarely catastrophic but does reduce the operating efficiency of machine components and structures. At this time of economic crisis, this is a very important field of study because of the huge impact the wear of materials has on the economy. The purpose of this book is to present a collection of examples illustrating the state of the art and research developments into the wear of advanced materials in several applications. It can be used as a research book for a final undergraduate engineering course (for example into materials, mechanics, etc.) or as the focus of the effect of wear on advanced materials at a postgraduate level. It can also serve as a useful reference for academics, biomaterials researchers, mechanical and materials engineers, and professionals in related spheres working with tribology and advanced materials.Table of ContentsPreface xi Chapter 1. Carbon Fabric-reinforced Polymer Composites and Parameters Controlling Tribological Performance 1 Jayashree BIJWE and Mohit SHARMA 1.1. Introduction to polymeric tribo-composites 3 1.2. Carbon fibers as reinforcement 6 1.3. Carbon fabric-reinforced composites 12 1.4. Tribo-performance of CFRCs: influential parameters 15 1.5. Concluding remarks 46 1.6. Bibliography 50 A1.1. Appendix I: Various techniques for developing CFRCs by compression molding 54 A2. Appendix II: Characterization methods for CFRCs 57 Chapter 2. Adhesive Wear Characteristics of Natural Fiber-reinforced Composites 61 Belal F. YOUSIF 2.1. Introduction 62 2.2. Preparation of polyester composites 67 2.3. Specifications of the fibers and composites 70 2.4. Tribo-experimental details 76 2.5. Summary 93 2.6. Bibliography 94 Chapter 3. Resistance to Cavitation Erosion: Material Selection 99 Jinjun LU, Zhen LI, Xue GONG, Jiesheng HAN and Junhu MENG 3.1. Cavitation erosion of materials – a brief review 99 3.2. Measuring the wear resistance of a material to cavitation erosionby using a vibratory cavitation erosion apparatus 101 3.3. Material selection 108 3.4. Conclusion 115 3.5. Acknowledgement 116 3.6. Bibliography 116 Chapter 4. Cavitation of Biofuel Applied in the Injection Nozzles of Diesel Engines 119 Hengzhou WO, Xianguo HU, Hu WANG and Yufu XU 4.1. Introduction 120 4.2. General understanding of cavitation erosion 122 4.3. Hydraulic characteristics of cavitation flow 131 4.4. Influence of fuel property on cavitation 139 4.5. Cavitation erosion of biofuel in the diesel injection nozzle 146 4.6. Conclusion 155 4.7. Acknowledgments 156 4.8. Bibliography 157 Chapter 5. Wear and Corrosion Damage of Medical-grade Metals and Alloys 163 Jae-Joong RYU and Pranav SHROTRIYA 5.1. Introduction 164 5.2. Clinical studies and mechanistic investigation into implant failure 173 5.3. Residual stress development by rough surface contact 184 5.4. Conclusion 192 5.5. Bibliography 193 List of Authors 197 Index 201

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Book SynopsisMachinability of Advanced Materials addresses the level of difficulty involved in machining a material, or multiple materials, with the appropriate tooling and cutting parameters. A variety of factors determine a material’s machinability, including tool life rate, cutting forces and power consumption, surface integrity, limiting rate of metal removal, and chip shape. These topics, among others, and multiple examples comprise this research resource for engineering students, academics, and practitioners.Table of ContentsPreface ix Chapter 1. Machinability: Existing and Advanced Concepts 1 Viktor P. Astakhov Chapter 2. Milling Burr Formation and Avoidance 57 Seyed A. Niknam, Walery Wygowski, Marek Balazinksi and Victor Songmene Chapter 3. Machinability of Titanium and Its Alloys 95 Ali Hosseini, Hossam A. Kishawy and Hussein M. Hussein Chapter 4. Effects of Alloying Elements on the Machinability of Near-Eutectic Al-Si Casting Alloys 119 Yasser Zedan, Saleh A. Alkahtani and Fawzy H. Samuel 5. The Machinability of Hard Materials – A Review 145 Paulo Campos, J. Paulo Davim, J. Roberto Ferreira, A. Paulo Paiva and P. Paulo Balestrassi Chapter 6. An Investigation of Ductile Regime Machining of Silicon Nitride Ceramics 175 Vijayan Krishnaraj and S. Senthil Kumar List of Authors 229 Index 233

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Book SynopsisMaking a decision, of any importance, is never simple. On the one hand, specialists in decision theory do not come within the reach of most policy makers and, secondly, there are very few books on pragmatic decision that are not purely anecdotal. In addition, there is virtually no book that provides a link between decision-making and action. This book provides a bridge between the latest results in artificial intelligence, neurobiology, psychology and decision-making for action. What is the role of intuition or emotion? What are the main psychological biases of which we must be wary? How can we avoid being manipulated? What is the proper use of planning? How can we remain rational even if one is not an expert in probabilities? Perhaps more importantly for managers, how does one go from decision to action? So many questions fundamental to the practice of decision-making are addressed. This book dissects all issues that arise almost daily for decision-makers, at least for major decisions. Drawing on numerous examples, this book answers, in plain language and imagery, all your questions. The final chapter takes the form of a brief reminder - everything you have to remember to be a good decision-maker.Table of ContentsIntroduction xi Chapter 1 What is a Decision, or What Does Decision Theory Have to Teach Us? 1 1.1 Actions and events 1 1.2 Probabilities 5 1.3 Expected utility 7 1.4 Subjective probabilities and rationality of the decision 12 1.5 Caveats and recommendations 14 Chapter 2 Scenarios and Conditional Probabilities 17 2.1 Scenarios 17 2.2 Compound probabilities 21 2.3 Scenarios and conditional probabilities 24 2.4 Decision tree 28 2.5 Scenarios, information and pragmatics 32 2.6 Pursuance of the scenarios and the "just one more push" 35 2.7 Conditional probabilities and accidents 39 2.8 Caveats and recommendations 41 Chapter 3 The Process of Decision-Making and its Rationality, or What Does Artificial Intelligence Have to Teach Us? 43 3.1 A decision as a problem 43 3.2 Decision table 45 3.3 The general process of decision-making 46 3.4 Case-based reasoning 48 3.5 The Olympian point-of-view, and H Simon’s view 51 3.6 Information 54 3.7 Limited rationality 57 3.8 Heuristics 60 3.9 Cognitive limitation 61 3.10 Feedback on rationality in decisions 62 3.11 Caveats and recommendations 64 Chapter 4 Intuition, Emotion, Recognition and Reasoning or, What Does the Neurobiology of Decision-Making Have to Teach Us? 67 4.1 Introduction 68 4.2 Animal "decision" 69 4.3 Recognition-primed decision 70 4.4 The brain and emotion 73 4.5 Short-term, long-term 78 4.6 The Bayesian brain 83 4.7 Caveats and recommendations 85 Chapter 5 Decision-Making in the Presence of Conflicting Criteria, or What Does a Multicriterion Decision Aid Have to Teach Us? 87 5.1 Preference structures 88 5.2 Multicriterion decision aid 91 5.3 Weighted sum aggregation 93 5.4 Other aggregation methods 100 5.5 Aggregation of votes 103 5.6 Social choice and collective decision 105 5.7 Individual reactions to multicriterion decision-making 109 5.8 Constraints and multicriterion decision-making in organizations 110 5.9 Caveats and recommendations 112 Chapter 6 The Decision-Maker’s Psychology, or What Does Psychology Have to Teach Us? 115 6.1 Introduction 116 6.2 The decision-maker’s rationality and utility function 117 6.3 Constructing the utility function 119 6.4 Utility function in the risk 120 6.5 Loss aversion and the endowment effect 125 6.6 Biases related to the probabilities 126 6.7 Self-confidence and the illusion of control 134 6.8 Biases linked to memory 136 6.9 Frame effect 140 6.10 Level of reference and anchoring 144 6.11 Rationalization and reinforcement 154 6.12 System 1 or System 2? 156 6.13 Biases or heuristics? 159 6.14 Caveats and recommendations 162 Chapter 7 Context of the Decision: Intention, Commitment, Trust, Fairness, Authority and Freedom 167 7.1 Intention and commitment 168 7.2 Trust and reciprocity 171 7.3 Fairness 177 7.4 Freedom and responsibility 180 7.5 Authority 182 7.6 "Leadership" in organizations 186 7.7 Rationality between logic and probabilities 189 7.8 Rationality and "good reasons" 192 7.9 Caveats and recommendations 197 Chapter 8 Action: Giving the Impetus or Managing 201 8.1 Deciding and acting 202 8.2 Quick or slow decision-makers 203 8.3 Consensual or imperative decision-makers 208 8.4 To act or to manage? That is the question 212 8.5 Reflect long, project long term: strategic planning and decision-making in organizations 217 8.6 Feedback and learning 221 8.7 Conclusion 226 8.8 Caveats and recommendations 226 Chapter 9 Vade Mecum of the Acting Decision-Maker 229 9.1 That which depends on you, and that which does not 229 9.2 That which depends on you: information, imagination and the process of decision-making 230 9.3 That which depends only on you: learning and planning 232 9.4 That which depends on nature: the pitfalls of probabilities 234 9.5 That which depends on our human nature: the pitfalls of the human brain 236 9.6 That which depends on other people: conflicts and manipulation 239 9.7 What the result depends on: your style and your action 241 9.8 And finally... 243 Bibliography 245 Index of Names 263 General Index 269

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Book SynopsisSince the middle of the 20th Century yield design approaches have been identified with the lower and upper bound theorem of limit analysis theory – a theory associated with perfect plasticity. This theory is very restrictive regarding the applicability of yield design approaches, which have been used for centuries for the stability of civil engineering structures. This book presents a theory of yield design within the original “equilibrium/resistance” framework rather than referring to the theories of plasticity or limit analysis; expressing the compatibility between the equilibrium of the considered structure and the resistance of its constituent material through simple mathematical arguments of duality and convex analysis results in a general formulation, which encompasses the many aspects of its implementation to various stability analysis problems. After a historic outline and an introductory example, the general theory is developed for the three-dimensional continuum model in a versatile form based upon simple arguments from the mathematical theory of convexity. It is then straightforwardly transposed to the one-dimensional curvilinear continuum, for the yield design analysis of beams, and the two-dimensional continuum model of plates and thin slabs subjected to bending. Field and laboratory observations of the collapse of mechanical systems are presented along with the defining concept of the multi-parameter loading mode. The compatibility of equilibrium and resistance is first expressed in its primal form, on the basis of the equilibrium equations and the strength domain of the material defined by a convex strength criterion along with the dual approach in the field of potentially safe loads, as is the highlighting of the role implicitly played by the theory of yield design as the fundamental basis of the implementation of the ultimate limit state design (ULSD) philosophy with the explicit introduction of resistance parameters. Contents 1. Origins and Topicality of a Concept. 2. An Introductory Example of the Yield Design Approach. 3. The Continuum Mechanics Framework. 4. Primal Approach of the Theory of Yield Design. 5. Dual Approach of the Theory of Yield Design. 6. Kinematic Exterior Approach. 7. Ultimate Limit State Design from the Theory of Yield Design. 8. Optimality and Probability Approaches of Yield Design. 9. Yield Design of Structures. 10. Yield Design of Plates: the Model. 11. Yield Design of Plates Subjected to Pure Bending. About the Authors Jean Salençon is Emeritus Professor at École polytechnique and École des ponts et chaussées, ParisTech, France. Since 2009 he has been a member of the Administrative Board of CNRS (Paris, France). He has received many awards including the Légion d’Honneur (Commander), Ordre National du Mérite (Officer) and Palmes Académiques (Commander). His research interests include structure analysis, soil mechanics and continuum mechanics.Table of ContentsPreface xi Chapter 1. Origins and Topicality of a Concept 1 1.1. Historical milestones 1 1.2. Topicality of the yield design approach 8 1.3. Bibliography 11 Chapter 2. An Introductory Example of the Yield Design Approach 19 2.1. Setting the problem 19 2.2. Potential stability of the structure 22 2.3. To what extent potential stability is a relevant concept? 24 2.4. Bibliography 28 Chapter 3. The Continuum Mechanics Framework 29 3.1. Modeling the continuum 29 3.2. Dynamics 34 3.3. The theory of virtual work 41 3.4. Statically and kinematically admissible fields 46 3.5. Bibliography 48 Chapter 4. Primal Approach of the Theory of Yield Design 51 4.1. Settlement of the problem 51 4.2. Potentially safe loads 57 4.3. Comments 60 4.4. Some usual isotropic strength criteria 66 4.5. Bibliography 70 Chapter 5. Dual Approach of the Theory of Yield Design 73 5.1. A static exterior approach 73 5.2. A kinematic necessary condition 76 5.3. The π functions 78 5.4. π functions for usual isotropic strength criteria 84 5.5. Bibliography 88 Chapter 6. Kinematic Exterior Approach 91 6.1. Equation of the kinematic exterior approach 91 6.2. Relevant virtual velocity fields 94 6.3. One domain, two approaches 100 6.4. Bibliography 107 Chapter 7. Ultimate Limit State Design from the Theory of Yield Design 111 7.1. Basic principles of ultimate limit state design 111 7.2. Revisiting the yield design theory in the context of ULSD 113 7.3. The yield design theory applied to ULSD 114 7.4. Conclusion 117 7.5. Bibliography 118 Chapter 8. Optimality and Probability Approaches of Yield Design 119 8.1. Optimal dimensioning and probabilistic approach 119 8.2. Domain of potential stability 120 8.3. Optimal dimensioning 130 8.4. Probabilistic approach of yield design 133 8.5. Bibliography 141 Chapter 9. Yield Design of Structures 145 9.1. The curvilinear one-dimensional continuum 145 9.2. Implementation of the yield design theory 157 9.3. Typical strength criteria 164 9.4. Final comments 172 9.5. Bibliography 174 Chapter 10. Yield Design of Plates: the Model 177 10.1. Modeling plates as two-dimensional continua 177 10.2. Dynamics 182 10.3. Theorem/principle of virtual work 191 10.4. Plate model derived from the three-dimensional continuum 198 10.5. Bibliography 204 Chapter 11. Yield Design of Plates Subjected to Pure Bending 205 11.1. The yield design problem 205 11.2. Implementation of the yield design theory 208 11.3. Strength criteria and π functions 213 11.4. Final comments 226 11.5. Bibliography 234 Index 237

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Book SynopsisWall turbulence control is a major subject, the investigation of which involves significant industrial, environmental and fundamental consequences. Wall Turbulence Control addresses recent advances achieved in active and passive wall turbulence control over the past two decades. This valuable reference for scientists, researchers and engineers provides an updated view of the research into this topic, including passive control, optimal and suboptimal control methodology, linear control and control using adaptive methods (neural networks), polymer and bubble injection, electromagnetic control and recent advances in control by plasma.Table of ContentsPreface vii Notations ix Chapter 1. General Points 1 1.1. Introduction 1 1.2. Tools to analyze and develop control strategies 2 1.2.1. Numerical simulations 2 1.2.2. Sensors 3 1.2.3. Actuators 20 Chapter 2. Summary of the Main Characteristics of Wall Turbulence 23 2.1. Introduction 23 2.2. General equations 23 2.2.1. Eulerian relations 24 2.3. Notations 25 2.4. Reynolds equations 26 2.5. Exact relations and FIK identity 27 2.6. Equations for a turbulent boundary layer 32 2.7. Scales in a turbulent wall flow 34 2.8. Turbulent viscosity closures 35 2.9. Turbulent intensities of the velocity components 47 2.10. Vorticity and near wall coherent structures 51 Chapter 3. Passive Control 65 3.1. Introduction 65 3.2. Large eddy (outer layer) breakup devices, LEBUs (OLDs) 66 3.2.1. General 66 3.2.2. Alteration of the inner structure by outer layer devices 67 3.3. Riblets 72 3.3.1. General 72 3.3.2. Effect of the riblets on the fine structure of wall turbulence 76 3.3.3. Effect of the protrusion height 84 3.4. Superhydrophobic surfaces 93 Chapter 4. Active Control 99 4.1. Introduction 99 4.2. Local blowing 100 4.3. Ad-hoc control 107 4.4. Transverse wall oscillations 115 4.5. Alternated spanwise Lorenz forcing and electromagnetic (EM) control 123 4.6. Extensions of spanwise forcing 131 4.7. Reynolds number dependence 132 4.8. Suboptimal active control 134 4.9. Optimal active control 143 4.10. Optimal linear control 147 4.11. Neural networks 156 4.12. Stochastic synchronization of the wall turbulence and dual control 157 Bibliography 167 Index 185

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Book SynopsisThis book presents a physical approach to the diffraction phenomenon and its applications in materials science. An historical background to the discovery of X-ray diffraction is first outlined. Next, Part 1 gives a description of the physical phenomenon of X-ray diffraction on perfect and imperfect crystals. Part 2 then provides a detailed analysis of the instruments used for the characterization of powdered materials or thin films. The description of the processing of measured signals and their results is also covered, as are recent developments relating to quantitative microstructural analysis of powders or epitaxial thin films on the basis of X-ray diffraction. Given the comprehensive coverage offered by this title, anyone involved in the field of X-ray diffraction and its applications will find this of great use.Table of ContentsPreface xi Acknowledgements xv An Historical Introduction: The Discovery of X-rays and the First Studies in X-ray Diffraction xvii Part 1. Basic Theoretical Elements, Instrumentation and Classical Interpretations of the Results 1 Chapter 1. Kinematic and Geometric Theories of X-ray Diffraction 3 1.1. Scattering by an atom 3 1.1.1. Scattering by a free electron 3 1.1.1.1. Coherent scattering: the Thomson formula 3 1.1.1.2. Incoherent scattering: Compton scattering [COM 23] 6 1.1.2. Scattering by a bound electron 8 1.1.3. Scattering by a multi-electron atom 11 1.2. Diffraction by an ideal crystal 14 1.2.1. A few elements of crystallography 14 1.2.1.1. Direct lattice 14 1.2.1.2. Reciprocal lattice 16 1.2.2. Kinematic theory of diffraction 17 1.2.2.1. Diffracted amplitude: structure factor and form factor 17 1.2.2.2. Diffracted intensity 18 1.2.2.3. Laue conditions [FRI 12] 22 1.2.3. Geometric theory of diffraction 23 1.2.3.1. Laue conditions 23 1.2.3.2. Bragg's law [BRA 13b, BRA 15] 24 1.2.3.3. The Ewald sphere 26 1.3. Diffraction by an ideally imperfect crystal 28 1.4. Diffraction by a polycrystalline sample 33 Chapter 2. Instrumentation used for X-ray Diffraction 39 2.1. The different elements of a diffractometer 39 2.1.1. X-ray sources 39 2.1.1.1. Crookes tubes 41 2.1.1.2. Coolidge tubes 42 2.1.1.3. High intensity tubes 47 2.1.1.4. Synchrotron radiation 49 2.1.2. Filters and monochromator crystals 52 2.1.2.1. Filters 52 2.1.2.2. Monochromator crystals 55 2.1.2.3. Multi-layered monochromators or mirrors 59 2.1.3. Detectors 62 2.1.3.1. Photographic film 62 2.1.3.2. Gas detectors 63 2.1.3.3. Solid detectors 68 2.2. Diffractometers designed for the study of powdered or bulk polycrystalline samples 72 2.2.1. The Debye-Scherrer and Hull diffractometer 73 2.2.1.1. The traditional Debye-Scherrer and Hull diffractometer 74 2.2.1.2. The modern Debye-Scherrer and Hill diffractometer: use of position sensitive detectors 76 2.2.2. Focusing diffractometers: Seeman and Bohlin diffractometers 87 2.2.2.1. Principle 87 2.2.2.2. The different configurations 88 2.2.3. Bragg-Brentano diffractometers 94 2.2.3.1. Principle 94 2.2.3.2. Description of the diffractometer; path of the X-ray beams 97 2.2.3.3. Depth and irradiated volume 103 2.2.4. Parallel geometry diffractometers 104 2.2.5. Diffractometers equipped with plane detectors 109 2.3. Diffractometers designed for the study of thin films 110 2.3.1. Fundamental problem 110 2.3.1.1. Introduction 110 2.3.1.2. Penetration depth and diffracted intensity 111 2.3.2. Conventional diffractometers designed for the study of polycrystalline films 116 2.3.3. Systems designed for the study of textured layers 118 2.3.4. High resolution diffractometers designed for the study of epitaxial films 120 2.3.5. Sample holder 123 2.4. An introduction to surface diffractometry 125 Chapter 3. Data Processing, Extracting Information 127 3.1. Peak profile: instrumental aberrations 129 3.1.1. X-ray source: g1(epsilon) 130 3.1.2. Slit: g2(epsilon) 130 3.1.3. Spectral width: g3(epsilon) 131 3.1.4. Axial divergence: g4(epsilon) 131 3.1.5. Transparency of the sample: g5(epsilon) 133 3.2. Instrumental resolution function 135 3.3. Fitting diffraction patterns 138 3.3.1. Fitting functions 138 3.3.1.1. Functions chosen a priori 138 3.3.1.2. Functions calculated from the physical characteristics of the diffractometer 143 3.3.2. Quality standards 144 3.3.3. Peak by peak fitting 145 3.3.4. Whole pattern fitting 147 3.3.4.1. Fitting with cell constraints 147 3.3.4.2. Structural simulation: the Rietveld method 147 3.4. The resulting characteristic values 150 3.4.1. Position 151 3.4.2. Integrated intensity 152 3.4.3. Intensity distribution: peak profiles 153 Chapter 4. Interpreting the Results 155 4.1. Phase identification 155 4.2. Quantitative phase analysis 158 4.2.1. Experimental problems 158 4.2.1.1. Number of diffracting grains and preferential orientation 158 4.2.1.2. Differential absorption 161 4.2.2. Methods for extracting the integrated intensity 162 4.2.2.1. Measurements based on peak by peak fitting 162 4.2.2.2. Measurements based on the whole fitting of the diagram 163 4.2.3. Quantitative analysis procedures 165 4.2.3.1. The direct method 165 4.2.3.2. External control samples 166 4.2.3.3. Internal control samples 166 4.3. Identification of the crystal system and refinement of the cell parameters 167 4.3.1. Identification of the crystal system: indexing 167 4.3.2. Refinement of the cell parameters 171 4.4. Introduction to structural analysis 172 4.4.1. General ideas and fundamental concepts 173 4.4.1.1. Relation between the integrated intensity and the electron density 173 4.4.1.2. Structural analysis 175 4.4.1.3. The Patterson function 177 4.4.1.4. Two-dimensional representations of the electron density distribution 180 4.4.2. Determining and refining structures based on diagrams produced with polycrystalline samples 183 4.4.2.1. Introduction 183 4.4.2.2. Measuring the integrated intensities and establishing a structural model 184 4.4.2.3. Structure refinement: the Rietveld method 185 Part 2. Microstructural Analysis 195 Chapter 5. Scattering and Diffraction on Imperfect Crystals 197 5.1. Punctual defects 197 5.1.1. Case of a crystal containing randomly placed vacancies causing no relaxation 198 5.1.2. Case of a crystal containing associated vacancies 201 5.1.3. Effects of atom position relaxations 203 5.2. Linear defects, dislocations 205 5.2.1. Comments on the displacement term 207 5.2.2. Comments on the contrast factor 210 5.2.3. Comments on the factor f(M) 212 5.3. Planar defects. 212 5.4. Volume defects 218 5.4.1. Size of the crystals 218 5.4.2. Microstrains 226 5.4.3. Effects of the grain size and of the microstrains on the peak profiles: Fourier analysis of the diffracted intensity distribution 231 Chapter 6. Microstructural Study of Randomly Oriented Polycrystalline Samples 235 6.1. Extracting the pure profile 236 6.1.1. Methods based on deconvolution 237 6.1.1.1. Constraint free deconvolution method: Stokes' method 238 6.1.1.2. Deconvolution by iteration 242 6.1.1.3. Stabilization methods 244 6.1.1.4. The maximum entropy or likelihood method, and the Bayesian method 244 6.1.1.5. Methods based on a priori assumptions on the profile 245 6.1.2. Convolutive methods 246 6.2. Microstructural study using the integral breadth method 247 6.2.1. The Williamson-Hall method 248 6.2.2. The modified Williamson-Hall method and Voigt function fitting 250 6.2.3. Study of size anisotropy 252 6.2.4. Measurement of stacking faults 255 6.2.5. Measurements of integral breadths by whole pattern fitting 257 6.3. Microstructural study by Fourier series analysis of the peak profiles 262 6.3.1. Direct analysis: the Bertaut-Warren-Averbach method 262 6.3.2. Indirect Fourier analysis 268 6.4. Microstructural study based on the modeling of the diffraction peak profiles 270 Chapter 7. Microstructural Study of Thin Films 275 7.1. Positioning and orienting the sample 276 7.2. Study of disoriented or textured polycrystalline films 279 7.2.1. Films comprised of randomly oriented crystals 279 7.2.2. Studying textured films 285 7.2.2.1. Determining the texture 285 7.2.2.2. Quantification of the crystallographic orientation: studying texture 289 7.3. Studying epitaxial films 292 7.3.1. Studying the crystallographic orientation and determining epitaxy relations 292 7.3.1.1. Measuring the normal orientation: rocking curves 293 7.3.1.2. Measuring the in-plane orientation: phi-scan 295 7.3.2. Microstructural studies of epitaxial films 300 7.3.2.1. Reciprocal space mapping and methodology 304 7.3.2.2. Quantitative microstructural study by fitting the intensity distributions with Voigt functions 307 7.3.2.3. Quantitative microstructural study by modeling of one-dimensional intensity distributions 312 Bibliography 319 Index 349

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Book SynopsisThree aspects are developed in this book: modeling, a description of the phenomena and computation methods. A particular effort has been made to provide a clear understanding of the limits associated with each modeling approach. Examples of applications are used throughout the book to provide a better understanding of the material presented.Table of ContentsPreface 13 Chapter 1. Vibrations of Continuous Elastic Solid Media 17 1.1. Objective of the chapter 17 1.2. Equations of motion and boundary conditions of continuous media 18 1.2.1. Description of the movement of continuous media 18 1.2.2. Law of conservation 21 1.2.3. Conservation of mass 23 1.2.4. Conservation of momentum 23 1.2.5. Conservation of energy 25 1.2.6. Boundary conditions 26 1.3. Study of the vibrations: small movements around a position of static, stable equilibrium 28 1.3.1. Linearization around a configuration of reference 28 1.3.2. Elastic solid continuous media 32 1.3.3. Summary of the problem of small movements of an elastic continuous medium in adiabatic mode 33 1.3.4. Position of static equilibrium of an elastic solid medium 34 1.3.5. Vibrations of elastic solid media 35 1.3.6. Boundary conditions 37 1.3.7. Vibrations equations 38 1.3.8. Notes on the initial conditions of the problem of vibrations 39 1.3.9. Formulation in displacement 40 1.3.10. Vibration of viscoelastic solid media 40 1.4. Conclusion 44 Chapter 2. Variational Formulation for Vibrations of Elastic Continuous Media 45 2.1. Objective of the chapter 45 2.2. Concept of the functional, bases of the variational method 46 2.2.1. The problem 46 2.2.2. Fundamental lemma 46 2.2.3. Basis of variational formulation 47 2.2.4. Directional derivative 50 2.2.5. Extremum of a functional calculus 55 2.3. Reissner’s functional 56 2.3.1. Basic functional 56 2.3.2. Some particular cases of boundary conditions 59 2.3.3. Case of boundary conditions effects of rigidity and mass 60 2.4. Hamilton’s functional 61 2.4.1. The basic functional 61 2.4.2. Some particular cases of boundary conditions 62 2.5. Approximate solutions 63 2.6. Euler equations associated to the extremum of a functional 64 2.6.1. Introduction and first example 64 2.6.2. Second example: vibrations of plates 68 2.6.3. Some results 72 2.7. Conclusion 75 Chapter 3. Equation of Motion for Beams 77 3.1. Objective of the chapter 77 3.2. Hypotheses of condensation of straight beams 78 3.3. Equations of longitudinal vibrations of straight beams 80 3.3.1. Basic equations with mixed variables 80 3.3.2. Equations with displacement variables 85 3.3.3. Equations with displacement variables obtained by Hamilton’s functional 86 3.4. Equations of vibrations of torsion of straight beams 89 3.4.1. Basic equations with mixed variables 89 3.4.2. Equation with displacements 91 3.5. Equations of bending vibrations of straight beams 93 3.5.1. Basic equations with mixed variables: Timoshenko’s beam 93 3.5.2. Equations with displacement variables: Timoshenko’s beam 97 3.5.3. Basic equations with mixed variables: Euler-Bernoulli beam 101 3.5.4. Equations of the Euler-Bernoulli beam with displacement variable 102 3.6. Complex vibratory movements: sandwich beam with a flexible inside 104 3.7. Conclusion 109 Chapter 4. Equation of Vibration for Plates 111 4.1. Objective of the chapter 111 4.2. Thin plate hypotheses 112 4.2.1. General procedure 112 4.2.2. In plane vibrations 112 4.2.3. Transverse vibrations: Mindlin’s hypotheses 113 4.2.4. Transverse vibrations: Love-Kirchhoff hypotheses 114 4.2.5. Plates which are non-homogenous in thickness 115 4.3. Equations of motion and boundary conditions of in plane vibrations 116 4.4. Equations of motion and boundary conditions of transverse vibrations 121 4.4.1. Mindlin’s hypotheses: equations with mixed variables 121 4.4.2. Mindlin’s hypotheses: equations with displacement variables 123 4.4.3. Love-Kirchhoff hypotheses: equations with mixed variables 124 4.4.4. Love-Kirchhoff hypotheses: equations with displacement variables 127 4.4.5. Love-Kirchhoff hypotheses: equations with displacement variables obtained using Hamilton’s functional 129 4.4.6. Some comments on the formulations of transverse vibrations 130 4.5. Coupled movements 130 4.6. Equations with polar co-ordinates 133 4.6.1. Basic relations 133 4.6.2. Love-Kirchhoff equations of the transverse vibrations of plates 135 4.7. Conclusion 138 Chapter 5. Vibratory Phenomena Described by the Wave Equation 139 5.1. Introduction 139 5.2. Wave equation: presentation of the problem and uniqueness of the solution 140 5.2.1. The wave equation 140 5.2.2. Equation of energy and uniqueness of the solution 142 5.3. Resolution of the wave equation by the method of propagation (d’Alembert’s methodology) 145 5.3.1. General solution of the wave equation 145 5.3.2. Taking initial conditions into account 147 5.3.3. Taking into account boundary conditions: image source 151 5.4. Resolution of the wave equation by separation of variables 154 5.4.1. General solution of the wave equation in the form of separate variables 154 5.4.2. Taking boundary conditions into account 157 5.4.3. Taking initial conditions into account 163 5.4.4. Orthogonality of mode shapes 165 5.5. Applications 168 5.5.1. Longitudinal vibrations of a clamped-free beam 168 5.5.2. Torsion vibrations of a line of shafts with a reducer 172 5.6. Conclusion 178 Chapter 6. Free Bending Vibration of Beams 181 6.1. Introduction 181 6.2. The problem 182 6.3. Solution of the equation of the homogenous beam with a constant cross-section 184 6.3.1. Solution 184 6.3.2. Interpretation of the vibratory solution, traveling waves, vanishing waves 186 6.4. Propagation in infinite beams 189 6.4.1. Introduction 189 6.4.2. Propagation of a group of waves 191 6.5. Introduction of boundary conditions: vibration modes 197 6.5.1. Introduction 197 6.5.2. The case of the supported-supported beam 197 6.5.3. The case of the supported-clamped beam 201 6.5.4. The free-free beam 206 6.5.5. Summary table 209 6.6. Stress-displacement connection 210 6.7. Influence of secondary effects 211 6.7.1. Influence of rotational inertia 212 6.7.2. Influence of transverse shearing 215 6.7.3. Taking into account shearing and rotational inertia 221 6.8. Conclusion 227 Chapter 7. Bending Vibration of Plates 229 7.1. Introduction 229 7.2. Posing the problem: writing down boundary conditions 230 7.3. Solution of the equation of motion by separation of variables 234 7.3.1. Separation of the space and time variables 234 7.3.2. Solution of the equation of motion by separation of space variables 235 7.3.3. Solution of the equation of motion (second method) 237 7.4. Vibration modes of plates supported at two opposite edges 239 7.4.1. General case 239 7.4.2. Plate supported at its four edges 241 7.4.3. Physical interpretation of the vibration modes 244 7.4.4. The particular case of square plates 248 7.4.5. Second method of calculation 251 7.5. Vibration modes of rectangular plates: approximation by the edge effect method 254 7.5.1. General issues 254 7.5.2. Formulation of the method 255 7.5.3. The plate clamped at its four edges 259 7.5.4. Another type of boundary conditions 261 7.5.5. Approximation of the mode shapes 263 7.6. Calculation of the free vibratory response following the application of initial conditions 263 7.7. Circular plates 265 7.7.1. Equation of motion and solution by separation of variables 265 7.7.2. Vibration modes of the full circular plate clamped at the edge 272 7.7.3. Modal system of a ring-shaped plate 276 7.8. Conclusion 277 Chapter 8. Introduction to Damping: Example of the Wave Equation 279 8.1. Introduction 279 8.2. Wave equation with viscous damping 281 8.3. Damping by dissipative boundary conditions 287 8.3.1. Presentation of the problem 287 8.3.2. Solution of the problem 288 8.3.3. Calculation of the vibratory response 294 8.4. Viscoelastic beam 297 8.5. Properties of orthogonality of damped systems 303 8.6. Conclusion 308 Chapter 9. Calculation of Forced Vibrations by Modal Expansion 309 9.1. Objective of the chapter 309 9.2. Stages of the calculation of response by modal decomposition 310 9.2.1. Reference example 310 9.2.2. Overview 317 9.2.3. Taking damping into account 321 9.3. Examples of calculation of generalized mass and stiffness 322 9.3.1. Homogenous, isotropic beam in pure bending 322 9.3.2. Isotropic homogenous beam in pure bending with a rotational inertia effect 323 9.4. Solution of the modal equation 324 9.4.1. Solution of the modal equation for a harmonic excitation 324 9.4.2. Solution of the modal equation for an impulse excitation 330 9.4.3. Unspecified excitation, solution in frequency domain 332 9.4.4. Unspecified excitation, solution in time domain 333 9.5. Example response calculation 336 9.5.1. Response of a bending beam excited by a harmonic force 336 9.5.2. Response of a beam in longitudinal vibration excited by an impulse force (time domain calculation) 340 9.5.3. Response of a beam in longitudinal vibrations subjected to an impulse force (frequency domain calculation) 343 9.6. Convergence of modal series 347 9.6.1. Convergence of modal series in the case of harmonic excitations 347 9.6.2. Acceleration of the convergence of modal series of forced harmonic responses 350 9.7. Conclusion 353 Chapter 10. Calculation of Forced Vibrations by Forced Wave Decomposition 355 10.1. Introduction 355 10.2. Introduction to the method on the example of a beam in torsion 356 10.2.1. Example: homogenous beam in torsion 356 10.2.2. Forced waves 358 10.2.3. Calculation of the forced response 359 10.2.4. Heterogenous beam 361 10.2.5. Excitation by imposed displacement 363 10.3. Resolution of the problems of bending 365 10.3.1. Example of an excitation by force 365 10.3.2. Excitation by torque 368 10.4. Damped media (case of the longitudinal vibrations of beams) 369 10.4.1. Example 369 10.5. Generalization: distributed excitations and non-harmonic excitations 371 10.5.1. Distributed excitations 371 10.5.2. Non-harmonic excitations 375 10.5.3. Unspecified homogenous mono-dimensional medium 377 10.6 Forced vibrations of rectangular plates 379 10.7. Conclusion 385 Chapter 11. The Rayleigh-Ritz Method based on Reissner’s Functional 387 11.1. Introduction 387 11.2. Variational formulation of the vibrations of bending of beams 388 11.3. Generation of functional spaces 391 11.4. Approximation of the vibratory response 392 11.5. Formulation of the method 392 11.6. Application to the vibrations of a clamped-free beam 397 11.6.1. Construction of a polynomial base 397 11.6.2. Modeling with one degree of freedom 399 11.6.3. Model with two degrees of freedom 402 11.6.4. Model with one degree of freedom verifying the displacement and stress boundary conditions 404 11.7. Conclusion 406 Chapter 12. The Rayleigh-Ritz Method based on Hamilton’s Functional 409 12.1. Introduction 409 12.2. Reference example: bending vibrations of beams 409 12.2.1 Hamilton’s variational formulation 409 12.2.2. Formulation of the Rayleigh-Ritz method 411 12.2.3. Application: use of a polynomial base for the clamped-free beam 414 12.3. Functional base of the finite elements type: application to longitudinal vibrations of beams 415 12.4. Functional base of the modal type: application to plates equipped with heterogenities 420 12.5. Elastic boundary conditions 423 12.5.1. Introduction 423 12.5.2. The problem 423 12.5.3. Approximation with two terms 424 12.6. Convergence of the Rayleigh-Ritz method 426 12.6.1. Introduction 426 12.6.2. The Rayleigh quotient 426 12.6.3. Introduction to the modal system as an extremum of the Rayleigh quotient 428 12.6.4. Approximation of the normal angular frequencies by the Rayleigh quotient or the Rayleigh-Ritz method 431 12.7. Conclusion 432 Bibliography and Further Reading 435 Index 439

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Book SynopsisThis book showcases the state of the art in the field of sensors and microsystems, revealing the impressive potential of novel methodologies and technologies. It covers a broad range of aspects, including: bio-, physical and chemical sensors; actuators; micro- and nano-structured materials; mechanisms of interaction and signal transduction; polymers and biomaterials; sensor electronics and instrumentation; analytical microsystems, recognition systems and signal analysis; and sensor networks, as well as manufacturing technologies, environmental, food and biomedical applications. The book gathers a selection of papers presented at the 20th AISEM National Conference on Sensors and Microsystems, held in Naples, Italy in February 2019, the event brought together researchers, end users, technology teams and policy makers.

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Book SynopsisThis volume gathers the latest advances, innovations and applications in the field of crack control in concrete, as presented by leading international researchers and engineers at the International RILEM Conference on Early-age and Long-term Cracking in RC Structures (CRC 2021), held in Paris, France on April 9, 2021. It covers early-age and long-term imposed deformations in concrete, analytical formulations for calculating crack widths in concrete, numerical simulations of early-age and long-term restrained behaviour of concrete elements, experimental investigations on cracking, on-site monitoring of imposed deformations and cracking, crack control and repair, and sustainability of design and remediation. The conference demonstrated that a comprehensive approach to this problem requires the design of robust experimental techniques, the development of multiscale models and the evaluation of code-based and other analytical approaches relevant to crack control in concrete. The contributions, which were selected through a rigorous international peer-review process, share exciting ideas that will spur novel research directions and foster new multidisciplinary collaborations.Table of Contents

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