Engineering: Mechanics of solids Books

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Book SynopsisConcisely examines the use of elasticity in solving geotechnical engineering problems. In a highly illustrated and user-friendly format, the book provides a thorough grounding in the linear theory of elasticity and an understanding of the applications, for upper level students in civil engineering and engineering geology.Trade Review"...this reviewer liked Elasticity and Geomechanics. The writing style is informal and reads easily....If an instructor is looking for a book on basic elasticity with a geomaterial focus, this reviewer would encourage that instructor to look at this work; he or she might be pleasantly surprised." E.B. Pitman, Applied Mechanics Reviews"...a valuable guide....Overall, a pleasantly readable book. Highly recommended...." ChoiceTable of Contents1. Some ideas from the theory of elasticity; 2. The elastic constants; 3. Fundamental solutions; 4. Applications of fundamental solutions; Appendices.

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Book SynopsisProfessor Achenbach discusses uses of reciprocity relations for the determination of elastodynamic fields, and presents a novel method to solve for wave fields by reciprocity of the actual field with a so-called virtual solution, shedding new light on the use of reciprocity relations for dynamic fields in elastic bodies.Trade Review'… this book provides a good basis for research workers in such fields who want to develop their knowledge in reciprocity formulations in elastodynamics.' ZAMM'This book is a delight to read. No matter how complicated a particular reasoning or derivation may be, every step is explained with insight and clarity that make the material easily accessible and enjoyable for beginners and experts alike. High-quality copyediting, printing, and page layout by Cambridge University Press complement this impression. If there has ever been a page-turner written on elastodynamics, this is the one.' Journal of Sound and VibrationTable of Contents1. Introduction; 2. Some elastodynamic theory; 3. Wave motion in an unbounded elastic solid; 4. Some simple applications of reciprocity; 5. Wave motion guided by a carrier wave; 6. Waves in an elastic layer; 7. Reciprocity considerations for the elastic layer; 8. Forced motion of an elastic layer; 9. Integral representations and integral equations; 10. Scattering waveguides and bounded bodies; Bibliography; Index.

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Book SynopsisValuable for both professionals and advanced undergraduate and graduate students, this second edition builds upon foundation courses in dynamics and strength of materials, developing several different methodologies for analysing collisions between structures, new general methods of solving multibody impact, and including new chapters and examples.Trade Review'… this is an excellent reference book for graduate-level students and professionals interested in non-colliding impacts. The rich theoretical content of this book alongside recent advances in experimental and numerical methods can provide engineers in particular with necessary knowledge and tools to design more effectively for complex impact problems.' Iman Mohagheghian, The Aeronautical JournalTable of Contents1. Introduction to analysis of low-speed impact; 2. Collinear rigid body impact; 3. Planar or 2-D rigid body impact; 4. 3-D impact of rough rigid bodies; 5. Tangential compliance in planar impact of rough bodies; 6. Continuum modeling for local deformation neat contact area; 7. Wave propagation from impact on slender deformable bodies; 8. Generalized impact analysis of multibody systems; 9. Viscoelastic or viscoplastic impact; 10. Impact against flexible structures; 11. Propagating transformations of state in self-organizing systems; 12. Impact of sports balls.

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Book SynopsisTheory of Dislocations provides unparalleled coverage of the fundamentals of dislocation theory, with applications to specific metal and ionic crystals. Rather than citing final results, step-by-step developments are provided to offer an in-depth understanding of the topic. The text provides the solid theoretical foundation for researchers to develop modeling and computational approaches to discrete dislocation plasticity, yet it covers important experimental observations related to the effects of crystal structure, temperature, nucleation mechanisms, and specific systems. This new edition incorporates significant advances in theory, experimental observations of dislocations, and new findings from first principles and atomistic treatments of dislocations. Also included are new discussions on thin films, deformation in nanostructured systems, and connection to crystal plasticity and strain gradient continuum formulations. Several new computer programs and worked problems allow the readeTrade Review'The classic book by Hirth and Lothe has been made much more assessable to a wider audience of students and researchers. The chapters include greatly expanded and improved illustrations. A complete set of worked solutions and supporting MATLAB codes for the problems at the end of each chapter, a set of Powerpoint files containing all figures in the book and Errata are all available at the Cambridge University Press website.' William D. Nix, Department of Materials Science and Engineering, Stanford UniversityTable of ContentsPart I. Isotropic Continua: 1. Introductory material; 2. Elasticity; 3. Theory of straight dislocations; 4. Theory of curved dislocations; 5. Applications to dislocation interactions; 6. Applications to self energies; 7. Dislocations at high velocities; Part II. Effects of Crystal Structure: 8. The influence of lattice periodicity; 9. Slip systems of perfect dislocations; 10. Partial dislocations in FCC metals; 11. Partial dislocations in other structures; 12. Dislocations in ionic crystals; 13. Dislocations in anisotropic elastic media; Part III. Interactions with Point Defects: 14. Equilibrium defect concentrations; 15. Diffusive glide and climb processes; 16. Glide of jogged dislocations; 17. Dislocation motion in vacancy supersaturations; 18. Effects of solute atoms on dislocation motion; Part IV. Groups of Dislocations: 19. Grain boundaries and interfaces; 20. Dislocation sources; 21. Dislocation pileups and cracks; 22. Dislocation intersections and barriers; 23. Deformation twinning.

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Book SynopsisUltrasonic guided waves in solid media are important in nondestructive testing and structural health monitoring, as new faster, sensitive, and economical ways of looking at materials and structures have become possible. This book can be read by managers from a 'black box' point of view, or used as a professional reference or textbook.Table of ContentsPreface; Acknowledgments; 1. Introduction; 2. Dispersion principles; 3. Unbounded isotropic and anisotropic media; 4. Reflection and refraction; 5. Oblique incidence; 6. Waves in plates; 7. Surface and subsurface waves; 8. Finite element method for guided wave mechanics; 9. The semi-analytical finite element method (SAFE); 10. Guided waves in hollow cylinders; 11. Circumferential guided waves; 12. Guided waves in layered structures; 13. Source influence on guided wave excitation; 14. Horizontal shear; 15. Guided waves in anisotropic media; 16. Guided wave phased arrays in piping; 17. Guided waves in viscoelastic media; 18. Ultrasonic vibrations; 19. Guided wave array transducers; 20. Introduction to guided wave nonlinear methods; 21. Guided wave imaging methods; Appendix A: ultrasonic nondestructive testing principles, analysis and display technology; Appendix B: basic formulas and concepts in the theory of elasticity; Appendix C: physically based signal processing concepts for guided waves; Appendix D: guided wave mode and frequency selection tips.

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Book SynopsisAn introduction to the mathematical basis of finite element analysis as applied to vibrating systems. Finite element analysis is a technique that is very important in modeling the response of structures to dynamic loads and is widely used in aeronautical, civil, and mechanical engineering as well as naval architecture.Trade Review"The contents of this work are very well organized, and Petyt (Univ. of Southhamption, UK) gradually introduces important concepts, making it a very useful theoretical reference." X. Le, Wentworth Institute of Technology"The contents of this work are very well organized ... a very useful theoretical reference. ...Recommended." CHOICETable of Contents1. Formulation of the equations of motion; 2. Element energy functions; 3. Introduction to the finite element displacement method; 4. In-plane vibration of plates; 5. Vibration of solids; 6. Flexural vibration of plates; 7. Vibration of stiffened plates and folded plate structures; 8. Vibration of shells; 9. Vibration of laminated plates and shells; 10. Hierarchical finite element method; 11. Analysis of free vibration; 12. Forced response; 13. Forced response II; 14. Computer analysis technique.

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Book SynopsisBeam theories are exploited worldwide to analyze civil, mechanical, automotive, and aerospace structures. Many beam approaches have been proposed during the last centuries by eminent scientists such as Euler, Bernoulli, Navier, Timoshenko, Vlasov, etc.Table of ContentsAbout the Authors ix Preface xi Introduction xiii References xvii 1 Fundamental equations of continuous deformable bodies 1 1.1 Displacement, strain, and stresses 1 1.2 Equilibrium equations in terms of stress components and boundary conditions 3 1.3 Strain displacement relations 4 1.4 Constitutive relations: Hooke’s law 4 1.5 Displacement approach via principle of virtual displacements 5 References 8 2 The Euler–Bernoulli and Timoshenko theories 9 2.1 The Euler–Bernoulli model 9 2.1.1 Displacement field 10 2.1.2 Strains 12 2.1.3 Stresses and stress resultants 12 2.1.4 Elastica 15 2.2 The Timoshenko model 16 2.2.1 Displacement field 16 2.2.2 Strains 16 2.2.3 Stresses and stress resultants 17 2.2.4 Elastica 18 2.3 Bending of a cantilever beam: EBBT and TBT solutions 18 2.3.1 EBBT solution 19 2.3.2 TBT solution 20 References 22 3 A refined beam theory with in-plane stretching: the complete linear expansion case 23 3.1 The CLEC displacement field 23 3.2 The importance of linear stretching terms 24 3.3 A finite element based on CLEC 28 Further reading 31 4 EBBT, TBT, and CLEC in unified form 33 4.1 Unified formulation of CLEC 33 4.2 EBBT and TBT as particular cases of CLEC 36 4.3 Poisson locking and its correction 38 4.3.1 Kinematic considerations of strains 38 4.3.2 Physical considerations of strains 38 4.3.3 First remedy: use of higher-order kinematics 39 4.3.4 Second remedy: modification of elastic coefficients 39 References 42 5 Carrera Unified Formulation and refined beam theories 45 5.1 Unified formulation 46 5.2 Governing equations 47 5.2.1 Strong form of the governing equations 47 5.2.2 Weak form of the governing equations 54 References 63 Further reading 63 6 The parabolic, cubic, quartic, and N-order beam theories 65 6.1 The second-order beam model, N =2 65 6.2 The third-order, N = 3, and the fourth-order, N = 4, beam models 67 6.3 N-order beam models 69 Further reading 71 7 CUF beam FE models: programming and implementation issue guidelines 73 7.1 Preprocessing and input descriptions 74 7.1.1 General FE inputs 74 7.1.2 Specific CUF inputs 79 7.2 FEM code 85 7.2.1 Stiffness and mass matrix 85 7.2.2 Stiffness and mass matrix numerical examples 91 7.2.3 Constraints and reduced models 95 7.2.4 Load vector 98 7.3 Postprocessing 100 7.3.1 Stresses and strains 101 References 103 8 Shell capabilities of refined beam theories 105 8.1 C-shaped cross-section and bending–torsional loading 105 8.2 Thin-walled hollow cylinder 107 8.2.1 Static analysis: detection of local effects due to a point load 109 8.2.2 Free-vibration analysis: detection of shell-like natural modes 112 8.3 Static and free-vibration analyses of an airfoil-shaped beam 116 8.4 Free vibrations of a bridge-like beam 119 References 121 9 Linearized elastic stability 123 9.1 Critical buckling load classic solution 123 9.2 Higher-order CUF models 126 9.2.1 Governing equations, fundamental nucleus 127 9.2.2 Closed form analytical solution 127 9.3 Examples 128 References 132 10 Beams made of functionally graded materials 133 10.1 Functionally graded materials 133 10.2 Material gradation laws 136 10.2.1 Exponential gradation law 136 10.2.2 Power gradation law 136 10.3 Beam modeling 139 10.4 Examples 141 References 148 11 Multi-model beam theories via the Arlequin method 151 11.1 Multi-model approaches 152 11.1.1 Mono-theory approaches 152 11.1.2 Multi-theory approaches 152 11.2 The Arlequin method in the context of the unified formulation 153 11.3 Examples 157 References 167 12 Guidelines and recommendations 169 12.1 Axiomatic and asymptotic methods 169 12.2 The mixed axiomatic–asymptotic method 170 12.3 Load effect 174 12.4 Cross-section effect 175 12.5 Output location effect 177 12.6 Reduced models for different error inputs 178 References 179 Index 181

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Book SynopsisThis book presents recent and cutting edge advances in our understanding of key aspects of the response of materials under extreme loads that take place during high velocity impact and penetration. The focus of the content is on the numerous challenges associated with characterization and modeling of complex interactions that occur during these highly dynamic events. The following specific topics, among others, are addressed: characterization of material behavior under extreme loadings (estimate of damage, effects related to moisture contents, large pressures, large strain rates, etc.); measurement of microstructural changes associated with damage and mesoscopic scale modeling; macroscopic modeling, using the framework of the theory of viscoplasticity and damage; modeling and simulation of localization, cracking, and dynamic fragmentation of materials; application to penetration mechanics and trajectory instabilities. The book gathers together selected papers based on work presented as invited lectures at the 2nd US-France symposium held on 28-30 May 2008 in Rocamadour, France. The conference was organized by Eric Buzaud (DGA, Centre d'Études de Gramat) under the auspices of the International Center for Applied Computational Mechanics (ICACM).Table of ContentsPreface xv Chapter 1. Geomaterials Under Extreme Loading: The Natural Case 1 Philippe LAMBERT and Hervé TRUMEL 1.1. Introduction 1 1.2. Natural impacts 2 1.3. Discussion 27 1.4. Conclusions 32 1.5. Bibliography 33 PART 1. EXPERIMENTAL CHARACTERIZATION 45 Chapter 2. The Shock Properties of Concrete and Related Materials 47 Kostas TSEMBELIS, David J. CHAPMAN, Christopher H. BRAITHWAITE, John E. FIELD and William G. PROUD 2.1. Introduction 47 2.2. Experimental studies 53 2.3. Conclusion 65 2.4. Acknowledgments 65 2.5. Bibliography 66 Chapter 3. Comparison of Shocked Sapphire and Alumina 69 Geremy KLEISER, Lalit CHHABILDAS and William REINHART 3.1. Abstract 69 3.2. Introduction 70 3.3. Material 71 3.4. Experimental method 72 3.5. Experimental results 73 3.6. Conclusions 84 3.7. Acknowledgments 84 3.8. Bibliography 84 Chapter 4. Observations of Ballistic Impact Damage in Glass Laminate 87 Stephan BLESS 4.1. Introduction 87 4.2. Transient measurements 88 4.3. Post-test measurements 90 4.4. Multiple impacts 97 4.5. Discussion and summary 97 4.6. Acknowledgments 98 4.7. Bibliography 98 Chapter 5. Experimental Analysis of Concrete Behavior Under High Confinement 101 Xuan Hong VU, Yann MALECOT, Laurent DAUDEVILLE and Eric BUZAUD 5.1. Introduction 101 5.2. Experimental device 102 5.3. Influence of the water/cement ratio 105 5.4. Influence of the coarse aggregate size 106 5.5. Influence of the cement paste volume 113 5.6. Conclusion and future work 116 5.7. Acknowledgment 118 5.8. Bibliography 118 Chapter 6. 3D Imaging and the Split Cylinder Fracture of Cement-Based Composites 121 Eric LANDIS 6.1. Introduction 121 6.2. Methods and materials 122 6.3. Experiments and analysis 126 6.4. Experimental results 128 6.5. Conclusions 129 6.6. Bibliography 130 Chapter 7. Testing Conditions on Kolsky Bar 131 Weinong CHEN 7.1. Introduction 131 7.2. Kolsky bar 132 7.3. Limitations of the Kolsky bar 133 7.4. Methods for conducting valid Kolsky bar experiments 136 7.5. Conclusions 142 7.6. Bibliography 143 PART 2. MATERIAL MODELING 145 Chapter 8. Experimental Approach and Modeling of the Dynamic Tensile Behavior of a Micro-Concrete 147 Pascal FORQUIN and Benjamin ERZAR 8.1. Introduction 147 8.2. Experimental device 149 8.3. Data processing 151 8.4. Experimental results 154 8.5. Modeling of the damage process in concrete at high strain-rates (the Denoual, Forquin, Hild model) 158 8.6. Conclusion 172 8.7. Bibliography 175 Chapter 9. Toward Physically-Based Explosive Modeling: Meso-Scale Investigations 179 Hervé TRUMEL, Philippe LAMBERT, Guillaume VIVIER and Yves SADOU 9.1. Introduction 179 9.2. Methodology 181 9.3. The material: microstructure and macroscopic mechanical behavior 182 9.4. Samples from unitary experiments 185 9.5. Analysis of a recovered target 193 9.6. Discussion 198 9.7. Conclusion and future work 204 9.8. Acknowledgments 204 9.9. Bibliography 204 Chapter 10. Coupled Viscoplastic Damage Model for Hypervelocity Impact Induced Damage in Metals and Composites 209 George Z. VOYIADJIS 10.1. Introduction 209 10.2. Theoretical preliminaries for high velocity impact 212 10.3. A coupled rate-dependent (viscoplasticity) continuum damage theory 214 10.4. Computational aspects of the proposed theory 220 10.5. Numerical applications 228 10.6. Conclusions 240 10.7. Bibliography 241 Chapter 11. High-Pressure Behavior of Concrete: Experiments and Elastic/Viscoplastic Modeling 247 Martin J. SCHMIDT, Oana CAZACU and Mark L. GREEN 11.1. Introduction 247 11.2. Experimental study 249 11.3. Elastic-viscoplastic model development 254 11.4. Conclusions 263 11.5. Bibliography 264 Chapter 12. The Virtual Penetration Laboratory: New Developments 267 Mark D. ADLEY, Andreas O. FRANK, Kent T. DANIELSON, Stephen A. AKERS, James L. O’DANIEL and Bruce PATTERSON 12.1. Introduction 267 12.2. Constitutive model development 268 12.3. Perforation simulations 278 12.4. Penetration simulations 282 12.5. CSPC penetration resistance equation 284 12.6. Conclusions 287 12.7. Acknowledgment 288 12.8. Bibliography 288 Chapter 13. Description of the Dynamic Fragmentation of Glass with a Meso-Damage Model 291 Xavier BRAJER, François HILD and Stéphane ROUX 13.1. Introduction 291 13.2. Experimental results 292 13.3. Fragmentation analysis 294 13.4. Microcracking analysis 299 13.5. A “meso-damage” approach 302 13.6. Conclusion 306 13.7. Acknowledgments 307 13.8. Bibliography 307 PART 3. NUMERICAL SIMULATION TECHNIQUES 311 Chapter 14. An Approach to Generate Random Localizations in Lagrangian Numerical Simulations 313 Jacques PETIT 14.1. Introduction 313 14.2. Numerical modeling 314 14.3. Electromagnetic compression and its regular use 318 14.4. Numerical simulations without rupture: copper and nickel samples 321 14.5. Numerical simulations with rupture: TA6V4 samples 323 14.6. Conclusion 328 14.7. Bibliography 330 Chapter 15. X-FEM for the Simulation of Dynamic Crack Propagation 333 Alain COMBESCURE 15.1. Energy conservation when a crack propagates: a key issue 333 15.2. Dynamic crack propagation laws 339 15.3. Experiments interpretation 341 15.4. Bibliography 348 Chapter 16. DEM Model of a Rigid Missile Impact on a Thin Concrete Slab 351 Frédéric DONZÉ, Wen-Jie SHIU and Laurent DAUDEVILLE 16.1. Introduction 351 16.2. The DEM model 353 16.3. Modeling of the impact tests 355 16.4. Influence of reinforcement ratio 358 16.5. Influence of the nose shape of missile 361 16.6. Conclusion 365 16.7. Bibliography 365 Chapter 17. The Lattice Discrete Particle Model (LDPM) for the Numerical Simulation of Concrete Behavior Subject to Penetration 369 Gianluca CUSATIS 17.1. Introduction 369 17.2. Review of LDPM formulation 371 17.3. Uniaxial compression strength tests 375 17.4. Three-point bending tests 377 17.5. Multiaxial compression strength tests 378 17.6. Hopkinson bar tests 380 17.7. Penetration through reinforced concrete slabs 382 17.8. Closing remark 384 17.9. Acknowledgments 385 17.10. Bibliography 385 Chapter 18. An Improved Contact Algorithm for Multi-Material Continuum Codes 389 Kenneth C. WALLS and David L. LITTLEFIELD 18.1. Introduction 389 18.2. Background 390 18.3. The contact-impact problem 391 18.4. Formulation 395 18.5. Finite element formulation 398 18.6. Calculations 401 18.7. Discussion 405 18.8. Conclusions 410 18.9. Bibliography 412 Chapter 19. Parallel Computing for Non-linear Concrete Modeling 415 Kent DANIELSON, Mark ADLEY and James O’DANIEL 19.1. Introduction 415 19.2. Explicit dynamic finite element analysis 416 19.3. Numerical methodologies 417 19.4. Numerical applications 421 19.5. Concluding remarks 429 19.6. Acknowledgments 430 19.7. Bibliography 431 List of Authors 433 Index 439

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Book SynopsisToday the fundamentals of solid mechanics may be explained by "numerical" experiments using the finite element method. The explanation is detailed in this book using many examples. After a short review of how the finite element method works (in Chapter 1), Chapter 2 develops some key points of solid mechanics: what is a beam? when and how can a structure be represented by beam elements? what are the basic hypotheses? what kind of information does a beam model provide? A generalized beam element is also presented. Chapter 3 uses the same approach for the discussion on stress concentrations and stress singularities: local effects; influence of geometric discontinuities, such as holes or corners; mesh refinements and/or analytic-numeric approaches. Chapter 4 is devoted to plate modeling: coupling of membrane and bending, folded, stiffened, composite plates. Chapter 5 provides a short presentation of the dynamics of structures with a particular focus on the modal method, the influence of local defaults on the modal response is also analyzed. Commercial software (Ansys) is used to study the examples.

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Book SynopsisThis timely book presents cutting-edge developments by experts in the field on the rapidly developing and scientifically challenging area of full-field measurement techniques used in solid mechanics – including photoelasticity, grid methods, deflectometry, holography, speckle interferometry and digital image correlation. The evaluation of strains and the use of the measurements in subsequent parameter identification techniques to determine material properties are also presented. Since parametric identification techniques require a close coupling of theoretical models and experimental measurements, the book focuses on specific modeling approaches that include finite element model updating, the equilibrium gap method, constitutive equation gap method, virtual field method and reciprocity gap method. In the latter part of the book, the authors discuss two particular applications of selected methods that are of special interest to many investigators: the analysis of localized phenomenon and connections between microstructure and constitutive laws. The final chapter highlights infrared measurements and their use in the mechanics of materials. Written and edited by knowledgeable scientists, experts in their fields, this book will be a valuable resource for all students, faculties and scientists seeking to expand their understanding of an important, growing research areaTable of ContentsForeword xv Michael A. SUTTON Introduction xvii Michel GRÉDIAC and François HILD Chapter 1. Basics of Metrology and Introduction to Techniques 1 André CHRYSOCHOOS and Yves SURREL 1.1. Introduction 1 1.2. Terminology: international vocabulary of metrology 2 1.2.1. Absolute or differential measurement 2 1.2.2. Main concepts 4 1.3. Spatial aspect 11 1.3.1. Spatial frequency 11 1.3.2. Spatial filtering 16 1.4. Classification of optical measurement techniques 18 1.4.1. White light measurement methods 19 1.4.2. Interference methods 21 1.4.3. Sensitivity vector 23 1.4.4. Synthetic sensitivity vectors 23 1.4.5. The different types of interferometric measurements 24 1.4.6. Holography, digital holography 27 1.4.7. Conclusion 28 1.5. Bibliography 29 Chapter 2. Photoelasticity 31 Fabrice BRÉMAND and Jean-Christophe DUPRÉ 2.1. Introduction 31 2.2. Concept of light polarization 32 2.3. Birefringence phenomenon 33 2.4. The law of optico-mechanics 34 2.5. Several types of polariscopes 35 2.5.1. Plane polariscope 35 2.5.2. Circular polariscope 38 2.5.3. White light polariscope 40 2.5.4. Photoelastic coating 40 2.6. Measurement of photoelastic constant C 42 2.7. Analysis by image processing 43 2.7.1. Using a plane polariscope 43 2.7.2. Using a circular polariscope 47 2.7.3. Using color images 48 2.8. Post-processing of photoelastic parameters 48 2.8.1. Drawing of isostatics or stress trajectories 48 2.8.2. Particular points 48 2.8.3. Stress separation and integration of the equilibrium equations 49 2.8.4. Comparison between experimentation and numerical modeling 50 2.9. Three-dimensional photoelasticity 50 2.9.1. The method of stress freezing and mechanical slicing 51 2.9.2. Optical slicing 52 2.9.3. Application example 56 2.10. Conclusion 57 2.11. Bibliography 57 Chapter 3. Grid Method, Moiré and Deflectometry 61 Jérôme MOLIMARD and Yves SURREL 3.1. Introduction 61 3.2. Principle 61 3.3. Surface encoding 63 3.4. Moiré 64 3.5. Phase detection 66 3.5.1. Global extraction procedure 66 3.5.2. Local phase detection: phase shifting 67 3.5.3. Measuring both components of the displacement 70 3.6. Sensitivity to out-of-plane displacements 71 3.7. Grid defects 72 3.8. Large deformation/large strain 73 3.8.1. Explicit method 73 3.8.2. Implicit method 74 3.8.3. Large strain 74 3.9. Fringe projection 75 3.10. Deflectometry 78 3.11. Examples 81 3.11.1. Off-axis tensile test of a unidirectional composite coupon 81 3.11.2. Rigid body displacement 83 3.11.3. SEM measurement 84 3.11.4. Characterization of lens distortion 85 3.12. Conclusion 88 3.13. Bibliography 89 Chapter 4. Digital Holography Methods 93 Pascal PICART and Paul SMIGIELSKI 4.1. Introduction 93 4.2. Basics of wave optics 94 4.2.1. Light diffraction 95 4.2.2. Interference 96 4.3. Basics of digital holography 97 4.3.1. Recording the hologram 97 4.3.2. Numerical reconstruction with the discrete Fresnel transform 99 4.3.3. Numerical reconstruction using convolution with adjustable magnification 100 4.3.4. Sensitivity vector 101 4.4. Basics of digital holographic interferometry 103 4.4.1. Phase difference 103 4.4.2. Spatial filtering of the phase and phase unwrapping 104 4.5. Digital holographic interferometry with spatial multiplexing 104 4.5.1. Principle 104 4.5.2. Theory 105 4.5.3. Experimental set-up 105 4.5.4. Application to synthetic concrete subjected to three-point bending 107 4.6. Digital color holography applied to three-dimensional measurements 112 4.6.1. Recording digital color holograms 112 4.6.2. Application to composite material subjected to a short beam test 113 4.7. Conclusion 118 4.8. Acknowledgment 119 4.9. Bibliography 119 Chapter 5. Elementary Speckle Interferometry 125 Pierre JACQUOT, Pierre SLANGEN and Dan BORZA 5.1. Introduction 125 5.2. What is speckle interferometry? 126 5.2.1. Simplified principle – correlation fringes 128 5.2.2. Speckle field and specklegram statistics in a nutshell 129 5.2.3. Speckle field transformation – small perturbation theory 131 5.2.4. Phase change-deformation law – sensitivity vector 132 5.2.5. Success or failure of experiments – central role of decorrelation 133 5.3. Optical point of view 134 5.4. Mechanical point of view: specific displacement field components 136 5.4.1. Measurement of the out-of-plane component 136 5.4.2. Measurement of the in-plane component [LEE 70] 137 5.4.3. 3C-3D: three components attached to three-dimensional objects 138 5.4.4. Partial derivatives of the displacement – shearography 139 5.4.5. Shape measurement and other considerations 140 5.5. Phase extraction 141 5.5.1. One-image methods 141 5.5.2. Phase-shifting methods 142 5.5.3. Advanced methods 143 5.5.4. Phase unwrapping 144 5.6. Dynamic deformations and vibrations 46 5.7. Setup calibration 148 5.7.1. Specifying the material point in object coordinates 149 5.7.2. Determination of the sensitivity vector 149 5.8. Specifications and limits 150 5.9. Final remarks, outlook and trends 151 5.10. Bibliography 153 Chapter 6. Digital Image Correlation 157 Michel BORNERT, François HILD, Jean-José ORTEU and Stéphane ROUX 6.1. Background 157 6.2. Surface and volume digital image correlation 158 6.2.1. Images 158 6.2.2. Texture of images 159 6.2.3. Guiding principles 161 6.2.4. Correlation coefficients 163 6.2.5. Subpixel interpolation 164 6.2.6. Local approaches 166 6.2.7. Optimization algorithms 168 6.2.8. Global approaches 169 6.3. Errors and uncertainties 172 6.3.1. Main error sources 172 6.3.2. Uncertainty and spatial resolution 173 6.3.3. Noise sensitivity 174 6.4. Stereo-correlation or 3D-DIC 175 6.4.1. The stereovision technique 176 6.4.2. 3D displacement measurement by stereo-correlation 180 6.4.3. Computation of surface strains from 3D displacements 181 6.4.4. Applications 182 6.5. Conclusions 182 6.6. Bibliography 183 Chapter 7. From Displacement to Strain 191 Pierre FEISSEL 7.1. Introduction 191 7.2. From measurement to strain 191 7.2.1. Three related steps 191 7.2.2. Framework for the differentiation of displacement measurements 192 7.2.3. The main families of methods for differentiating data 194 7.2.4. Quality of the reconstruction 195 7.3. Differentiation: difficulties illustrated for a one-dimensional example 197 7.3.1. A simple one-dimensional example 197 7.3.2. Finite differences 198 7.3.3. Global least squares – polynomial basis 199 7.3.4. Filtering through a convolution kernel 200 7.4. Approximation methods 203 7.4.1. General presentation 203 7.4.2. Global least squares – Finite element basis 204 7.4.3. Local least squares – polynomial basis 206 7.4.4. Three converging points of view 207 7.5. Behavior of the reconstruction methods 209 7.5.1. Splitting the reconstruction error 209 7.5.2. Estimation of approximation error 210 7.5.3. Estimation of random error 211 7.6. Selection criterion for the filtering parameters 214 7.6.1. Constant signal-to-noise ratio 214 7.6.2. A pragmatic criterion 216 7.7. Taking the time dimension into consideration 218 7.8. Concluding remarks 220 7.9. Bibliography 220 Chapter 8. Introduction to Identification Methods 223 Marc BONNET 8.1. Introduction 223 8.2. Identification and inversion: a conceptual overview 223 8.2.1. Inversion 223 8.2.2. Constitutive parameter identification 230 8.3. Numerical methods based on optimization 232 8.3.1. Gradient-based methods 232 8.3.2. Other methods 236 8.4. Methods specifically designed for full-field measurements: an overview 237 8.4.1. Finite element model updating 237 8.4.2. Constitutive relation error 238 8.4.3. Methods based on equilibrium satisfaction 239 8.4.4. Reciprocity gap 241 8.5. Conclusion 242 8.6. Bibliography 242 Chapter 9. Parameter Identification from Mechanical Field Measurements using Finite Element Model Updating Strategies 247 Emmanuel PAGNACCO, Anne-Sophie CARO-BRETELLE and Patrick IENNY 9.1. Introduction 247 9.2. Finite element method 249 9.2.1. Principles of the method 249 9.2.2. The “direct mechanical problem” and finite element analysis 252 9.3. Updating a finite element model for parameter identification 254 9.3.1. Theory 254 9.3.2. Objective functions and minimization procedure 256 9.3.3. Structural sensitivities 262 9.4. Applications, results and accuracy 264 9.4.1. Full-field measurements for the FEMU method 264 9.4.2. Application to the material behavior 265 9.4.3. Identification accuracy 267 9.5. Conclusion 268 9.6. Bibliography 269 Chapter 10. Constitutive Equation Gap 275 Stéphane PAGANO and Marc BONNET 10.1. Introduction 275 10.2. CEG in the linear elastic case: heterogeneous behavior and full-field measurement 276 10.2.1. First variant: exact enforcement of kinematic measurements 278 10.2.2. Second variant: enforcement of measurements by kinematic penalization 283 10.2.3. Comments 283 10.2.4. Some numerical examples 284 10.3. Extension to elastoplasticity 288 10.3.1. Formulation 288 10.3.2. Numerical method 290 10.4. Formulations based on the Legendre–Fenchel transform 293 10.5. Suitable formulations for dynamics or vibration 295 10.6. Conclusions 297 10.7. Bibliography 298 Chapter 11. The Virtual Fields Method 301 Michel GRÉDIAC, Fabrice PIERRON, Stéphane AVRIL, Evelyne TOUSSAINT and Marco ROSSI 11.1. Introduction 301 11.2. General principle 301 11.3. Constitutive equations depending linearly on the parameters: determination of the virtual fields 303 11.3.1. Introduction 303 11.3.2. Developing the PVW 303 11.3.3. Special virtual fields 305 11.3.4. Virtual fields optimized with respect to measurement noise 307 11.3.5. Virtual fields defined by subdomains 309 11.3.6. Examples 311 11.3.7. Plate bending 313 11.3.8. Large deformations: example of hyperelasticity 319 11.4. Case of constitutive equations that do not linearly depend on the constitutive parameters 321 11.4.1. Introduction 321 11.4.2. Elastoplasticity 321 11.4.3. Hyperelastic behavior 324 11.5. Conclusion 325 11.6. Bibliography 326 Chapter 12. Equilibrium Gap Method 331 Fabien AMIOT, Jean-Noël PÉRIÉ and Stéphane ROUX 12.1. Theoretical basis 331 12.1.1. Homogeneous elastic medium 332 12.1.2. Heterogeneous elastic medium 334 12.1.3. Incremental formulation 334 12.2. Finite difference implementation 335 12.3. Finite element implementation 337 12.4. Application to beam theory: local buckling 340 12.4.1. Application to beam theory 340 12.4.2. Loading identification 342 12.4.3. Identification of a heterogeneous stiffness field 343 12.5. Simultaneous identification of stiffness and loading fields 345 12.6. Spectral sensitivity and reconditioning 347 12.7. Damage 349 12.8. Application to a biaxial test carried out on a composite material 351 12.8.1. Damage modeling 352 12.8.2. Adapted expression of the reconditioned equilibrium gap 354 12.8.3. Application to a biaxial test 355 12.9. Exploitation of measurement uncertainty 358 12.10. Conclusions 359 12.11. Bibliography 360 Chapter 13. Reciprocity Gap Method 363 Stéphane ANDRIEUX, Huy Duong BUI and Andrei CONSTANTINESCU 13.1. Introduction 363 13.2. The reciprocity gap method 365 13.2.1. Definition of the reciprocity gap 367 13.2.2. Fundamental property of the reciprocity gap 367 13.3. Identification of cracks in electrostatics 368 13.3.1. Identification formulas for the plane of the crack(s) 370 13.3.2. Complete identification of cracks 371 13.4. Crack identification in thermoelasticity using displacement measurements 373 13.5. Conclusions and perspectives 377 13.6. Bibliography 378 Chapter 14. Characterization of Localized Phenomena 379 Jacques DESRUES and Julien RÉTHORÉ 14.1. Introduction 379 14.2. Definitions and properties of the localized phenomena being considered 380 14.3. Available methods for the experimental characterization of localized phenomena 386 14.3.1. Direct observation 386 14.3.2. Recording the coordinates of predefined markers 387 14.3.3. False relief photogrammetry 387 14.3.4. Digital image correlation 387 14.3.5. Digital volume correlation 388 14.3.6. X-ray tomography 388 14.4. Localization kinematics: a case study 390 14.4.1. Emergence and development of shear bands in a sand specimen under plane strain revealed by stereophotogrammetry 390 14.4.2. Comparison of stereophotogrammetry and digital image correlation for a biaxial test of a soft clay-rock specimen 391 14.4.3. The contribution of digital volume correlation to the detection of localization in isochoric shearing 393 14.4.4. Characterization of severe discontinuities: stereophotogrammetry and correlation 393 14.4.5. Localization on the grain scale: the contribution of discrete DVC 394 14.4.6. A fatigue crack in steel 395 14.4.7. Piobert–Lüders band in steel 395 14.4.8. Portevin–Le Châtelier band 396 14.5. The use of enriched kinematics 397 14.5.1. Displacement discontinuity 398 14.5.2. Strain discontinuity 399 14.6. Localization of the discontinuity zone 399 14.6.1. The use of strain fields 400 14.6.2. The use of correlation residuals 400 14.7. Identification of fracture parameters 401 14.8. Conclusion 405 14.9. Bibliography 406 Chapter 15. From Microstructure to Constitutive Laws 411 Jérôme CRÉPIN and Stéphane ROUX 15.1. Introduction 411 15.2. General problem 411 15.2.1. How can we appreciate spatial heterogeneity? 411 15.2.2. Phase segmentation 413 15.2.3. Inverse problem 413 15.2.4. Statistical description/morphological model 414 15.2.5. Coupling of identification with an exogenous field 417 15.3. Examples of local field characterization 418 15.3.1. EBSD analysis and orientation imaging microscopy 419 15.4. First example: elastic medium with microstructure 423 15.4.1. Glass wool 423 15.4.2. Identification 426 15.5. Second example: crystal plasticity 427 15.5.1. Multiscale approach for identification of material mechanical behavior 428 15.5.2. Methodology 430 15.5.3. Numerical simulation of mechanical behavior 431 15.6. Conclusions 434 15.7. Bibliography 435 Chapter 16. Thermographic Analysis of Material Behavior 439 Jean-Christophe BATSALE, André CHRYSOCHOOS, Hervé PRON and Bertrand WATTRISSE 16.1. Introduction 439 16.2. Thermomechanical framework 441 16.2.1. Constitutive equations 441 16.2.2. Heat equation 443 16.2.3. Energy balance over a load-unload cycle 444 16.3. Metrological considerations 446 16.3.1. Physics of radiation preliminaries 447 16.3.2. Calibration 448 16.3.3. Thermal noise and thermal drift 452 16.4. Heat diffusion models and identification methods 454 16.4.1. Diffusion equation for thin plates 454 16.4.2. Diffusion equation for straight beams 455 16.4.3. Diffusion equation for a monotherm material volume element 456 16.4.4. Integral transforms and quadrupole method related to thick media 457 16.5. Concluding comments and prospects 463 16.6. Bibliography 464 List of Authors 469 Index 475

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Book SynopsisComputational contact mechanics is a broad topic which brings together algorithmic, geometrical, optimization and numerical aspects for a robust, fast and accurate treatment of contact problems. This book covers all the basic ingredients of contact and computational contact mechanics: from efficient contact detection algorithms and classical optimization methods to new developments in contact kinematics and resolution schemes for both sequential and parallel computer architectures. The book is self-contained and intended for people working on the implementation and improvement of contact algorithms in a finite element software. Using a new tensor algebra, the authors introduce some original notions in contact kinematics and extend the classical formulation of contact elements. Some classical and new resolution methods for contact problems and associated ready-to-implement expressions are provided. Contents: 1. Introduction to Computational Contact. 2. Geometry in Contact Mechanics. 3. Contact Detection. 4. Formulation of Contact Problems. 5. Numerical Procedures. 6. Numerical Examples. About the Authors Vladislav A. Yastrebov is a postdoctoral-fellow in Computational Solid Mechanics at MINES ParisTech in France. His work in computational contact mechanics was recognized by the CSMA award and by the Prix Paul Caseau of the French Academy of Technology and Electricité de France.Table of ContentsForeword xi Preface xiii Notations xv Chapter 1. Introduction to Computational Contact 1 1.1. Historical remark 5 1.1.1. The augmented Lagrangian method 7 1.2. Basics of the numerical treatment of contact problems 9 1.2.1.Contact detection 9 1.2.2.Contact discretization 10 1.2.3.Contact resolution 13 Chapter 2. Geometry in ContactMechanics 15 2.1. Introduction 15 2.2. Interaction between contacting surfaces 19 2.2.1.Some notations 19 2.2.2.Normal gap 21 2.2.3.Closest point on a surface 26 2.2.4.Closest point on a curve 28 2.2.5.Shadow-projectionmethod 32 2.2.6.Tangential relative sliding 35 2.3. Variations of geometrical quantities 38 2.3.1.First-ordervariations 38 2.3.2. Second-order variations 40 2.4. Numericalvalidation 42 2.5. Discretized geometry 44 2.5.1. Shape functions andfinite elements 44 2.5.2. Geometryof contact elements 45 2.6. Enrichmentof contactgeometry 51 2.6.1. Derivation of enriched quantities 53 2.6.2. Variations of geometrical quantities 58 2.6.3.Exampleof enrichment 65 2.6.4.Concludingremarks 68 Chapter 3. Contact Detection 71 3.1. Introduction 71 3.2.All-to-all detection 76 3.2.1.Preliminaryphase 76 3.2.2.Detection phase 79 3.3.Bucket sort detection 84 3.3.1.Preliminaryphase 86 3.3.2.Numerical tests 87 3.3.3.Detection phase 90 3.3.4. Multi-face contact elements 91 3.3.5. Improvements 92 3.4. Case of unknown master–slave 93 3.5.Parallel contactdetection 97 3.5.1.General presentation 97 3.5.2. Single detection, multiple resolution approach 97 3.5.3. Multiple detection, multiple resolution approach 99 3.5.4. Scalability test 100 3.6.Conclusion 101 Chapter 4. Formulation of Contact Problems 103 4.1. Contact of a deformable solid with a rigid plane 103 4.1.1.Unilateral contactwith a rigid plane 104 4.1.2. Interpretation of contact conditions 109 4.1.3.Friction 111 4.1.4.An analogywith plastic flow 117 4.1.5. Interpretation of frictional conditions 121 4.2. Contact of a deformable solid with an arbitrary rigid surface 124 4.2.1. Non-penetration condition 125 4.2.2. Hertz–Signorini–Moreau’s contact conditions 129 4.2.3. Interpretation of contact conditions 130 4.2.4. Frictional conditions and their interpretation 132 4.2.5. Example: rheology of a one-dimensional frictional system on a sinusoidal rigid substrate 133 4.3. Contact between deformable solids 135 4.3.1. General formulation and variational inequality 135 4.3.2. Remarks on Coulomb’s frictional law 142 4.4. Variational equality and resolution methods 144 4.5. Penaltymethod 145 4.5.1.Frictionless case 145 4.5.2. Example 148 4.5.3. Nonlinearpenaltyfunctions 151 4.5.4. Frictional case 153 4.6. Method of Lagrange multipliers 157 4.6.1.Frictionless case 158 4.6.2. Frictional case 161 4.6.3. Example 164 4.7. AugmentedLagrangianMethod 170 4.7.1. Introduction 170 4.7.2.Applicationto contact problems 174 4.7.3.Example 183 Chapter 5. Numerical Procedures 189 5.1.Newton’smethod 189 5.1.1. One-dimensional Newton’s method 190 5.1.2. Multidimensional Newton’s method 193 5.1.3. Application to non-differentiable functions 195 5.1.4. Subdifferentials and subgradients 196 5.1.5 GeneralizedNewtonmethod 200 5.2. Returnmappingalgorithm 203 5.3. Finite elementmethod 210 5.3.1. Introduction 211 5.3.2.Contact elements 216 5.3.3. Discretization of the contact interface 219 5.3.4. Virtual work for discretized contact interface 220 5.3.5.Linearizationof equations 223 5.3.6.Example 225 5.4. Residual vectors and tangent matrices for contact elements 225 5.4.1. Penalty method: frictionless case 226 5.4.2. Penalty method: frictional case 228 5.4.3. Augmented Lagrangian method: frictionless case 237 5.4.4. Augmented Lagrangian method: frictional case 240 5.5. Method of partial Dirichlet–Neumann boundary conditions 248 5.5.1. Description of the numerical technique 248 5.5.2.Frictionless case 250 5.5.3.Frictional case 254 5.5.4.Remarks 255 5.6. Technicaldetails 255 5.6.1. Rigidmaster surface 256 5.6.2. Multi-face contact elements and smoothing techniques 257 5.6.3.Heterogeneous friction 260 5.6.4.Short remarks 261 Chapter 6. Numerical Examples 265 6.1.Two dimensionalproblems 265 6.1.1. Indentation by a rigid flat punch 265 6.1.2. Elastic disk embedded in an elastic bored plane 269 6.1.3. Indentation of an elastic rectangle by a circular indenter 272 6.1.4. Axisymmetricdeepcup drawing 274 6.1.5. Shallowironing 278 6.1.6. Axisymmetric post-buckling of a thin-walled cylinder 279 6.2. Three-dimensionalproblems 286 6.2.1. Accordion post-buckling folding of a thin-walled tube 286 6.2.2. Hydrostatic extrusion of a square plate through a circular hole 288 6.2.3. Frictional sliding of a cube on a rigid plane 292 Appendix 1. Vectors, Tensors and s-Structures 297 A1.1. Fundamentals 298 A1.2.Vector space basis 303 A1.2.1. Transformation matrices, covariant and contravariant objects 306 A1.2.2. Gradient operator or Hamilton’s operator 308 A1.3. Sub-basis, vector function of v-scalar argument 311 A1.4.Tensors 314 A1.5.Tensor as a linear operatoron vector space 322 A1.6.S-structures 325 A1.6.1. Formal definition, notations and types 327 A1.6.2.Simple operations 331 A1.6.3. Invariant s-structures 333 A1.6.4. Scalar products of v-vectors 336 A1.6.5. Inversev-vector 341 A1.6.6. Isomorphism of s-space and tensor space 343 A1.6.7. Tensor product of v-vectors 348 A1.7.Reducedformof s-structures 349 Appendix 2. Variations of Geometrical Quantities 353 A2.1.First-ordervariations 353 A2.1.1.Normal projectioncase 354 A2.1.2. Shadow-projection case: infinitely remote emitter 356 A2.1.3. Shadow-projection case: close emitter 361 A2.2. Second-order variations 362 A2.2.1.Normal projectioncase 362 A2.2.2. Shadow-projection case: infinitely remote emitter 369 A2.2.3. Shadow-projection case: close emitter 370 Bibliography 375 Index 387

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Book SynopsisDynamics of Civil Structures, Volume 2: Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics, 2020, the second volume of eight from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of the Dynamics of Civil Structures, including papers on:Structural VibrationHumans & Structures Innovative Measurement for Structural Applications Smart Structures and Automation Modal Identification of Structural Systems Bridges and Novel Vibration Analysis Sensors and Control

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