Classical mechanics Books

Book SynopsisVorwort.- Inhalt.- I Statik der Starrkörper.- 1 Mathematische Vorbereitungen. 2 Grundlagen. 3 Statik starrer Körper und Körpersysteme. 4 Kontinuierliche Kräfteverteilungen. 5 Haftung und Reibung. 6 Schnittgrößen.- II Elastostatik.- 7 Einführung in die indizierte Tensornotation. 8 Spannungen. 9 Verzerrungen. 10 Elastizität, Festigkeitshypothesen. 11 Elastische Verformung schlanker Körper.- III Dynamik.- 12 Noch einige mathematische Vorüberlegungen. 13 Kinematik. 14 Kinetik.- Anhang A Über den Umgang mit "infinitesimalen" Größen.- Anhang B Biographische Daten.- Anhang C Zum Studienbeginn.- Literaturverzeichnis.- Index

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Book SynopsisStatik.- 1 Erste Schritte. 2 Ebenes Kräftegleichgewicht am Punkt. 3 Statisches Gleichgewicht am ebenen starren Körper. 4 Räumliches Gleichgewicht. 5 Ebene Gelenksysteme. 6 Schnittgrößen. 7 Ebene Fachwerke. 8 Schwerpunkt. 9 Reibung. 10 Seilstatik. 11 Der Arbeitssatz. - Festigkeitslehre.- 12 Spannungen. 13 Verzerrungen. 14 Das Materialgesetz. 15 Zug- und Druckbeanspruchung. 16 Biegung. 17 Schub durch Querkraft. 18 Torsion. 19 Dünnwandige Behälter unter Innendruck. 20 Überlagerte Beanspruchung. 21 Energetische Methoden. 22 Euler'sches Knicken.- Anhang A: Lösungen der Aufgaben.- Anhang B: Literatur.- Anhang C: Kleine Formelsammlung Statik und Festigkeitslehre.- Stichwortverzeichnis.

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Book SynopsisDas Buch vermittelt die Grundlagen und wichtigsten Konzepte der Theoretischen Mechanik und Speziellen Relativitätstheorie, soweit sie in Lehramts- und Bachelorstudiengängen benötigt werden. Dabei handelt es sich nicht um eine im Sinne des Master- oder des früheren Diplomstudiums "möglichst umfassend" gehaltene Darstellung, sondern um eine - im Vergleich zu anderen Lehrbuchwerken zur Theoretischen Physik schlank gehaltene - Darlegung der theoretischen Grundpfeiler der modernen Physik.Table of ContentsKlassische Mechanik - Spezielle Relativitätstheorie - Lösungen und Lösungstipps zu den Aufgaben - Mathematischer Anhang - Einheiten und Konstanten

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Book Synopsis

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Book Synopsis

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Book SynopsisThese notes contain my lectures on light scattering by matter presented at the Scuola Normale Superiore, Pisa during May and June 1995. I have deleted some of the topics discussed then and added a few related to my recent work. The notes are not to be regarded as exhaustive but rather as a selection of topics. In particular I have discussed, as examples, the theoretical basis for the interpretation of experiment on light scattering by photons in alpha-quartz and by electronic excitations in boron-doped diamond.

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Book SynopsisExperiments on fracture of materials are made for various purposes. Of primary importance are those through which criteria predicting material failure by deformation and/or fracture are investigated. Since the demands of engineering application always precede the development of theories, there is another kind of experiment where conditions under which a particular material can fail are simulated as closely as possible to the operational situation but in a simplified and standardized form. In this way, many of the parameters corresponding to fracture such as toughness, Charpy values, crack opening distance (COD), etc. are measured. Obviously, a sound knowledge of the physical theories governing material failure is necessary as the quantity of interest can seldom be evaluated in a direct manner. Critical stress intensity factors and critical energy release rates are examples. Standard test of materials should be distinguished from basic experi­ ments. They are performed to provide routine information on materials responding to certain conditions of loading or environment. The tension test with or without a crack is among one of the most widely used tests. Because they affect the results, with size and shape of the specimen, the rate of loading, temperature and crack configuration are standardized to enable comparison and reproducibility of results. The American Society for Testing Materials (ASTM) provides a great deal of information on recommended procedures and methods of testing. The objective is to standardize specifications for materials and definition of technical terms.Table of Contents1 Stress concentrations.- 1.1 Introduction.- 1.2 Advantages and disadvantages of stress analysis methods used to determine stress concentrations.- 1.3 Compilation of results.- 1.4 Geometrically non-linear stress concentrations.- 1.5 Stress concentrations in mixed boundary value problems.- 1.6 Stress concentrations in some specific problems.- 1.7 Stress concentrations in three-dimensional problems.- 1.8 Dynamic stress concentrations.- 1.9 Unconventional approaches to the study of stress concentrations.- References.- 2 Use of photoelasticity in fracture mechanics.- 2.1 Introduction.- 2.2 Analytical foundations for cracked bodies.- 2.3 Experimental considerations.- 2.4 Application of the frozen stress method.- 2.5 Summary and conclusions.- References.- 3 Elastic stress intensity factors evaluated by caustics.- 3.1 Introduction.- 3.2 The basic formulas.- 3.3 The equations of caustics.- 3.4 Properties of the caustics at crack tips.- 3.5 The case of birefringent media.- 3.6 The case of anisotropic media.- 3.7 Interacting crack problems.- 3.8 Branched crack problems.- 3.9 Interface crack problems.- 3.10 V-notch problems.- 3.11 Shell problems.- 3.12 Plate problems.- 3.13 Other applications.- 3.14 Discussion.- 3.15 Conclusions.- References.- 4 Three-dimensional photoelasticity: stress distribution around a through thickness crack.- 4.1 Introduction.- 4.2 Hartranft-Sih plate theory.- 4.3 Triaxial crack border stress field.- 4.4 Experimental considerations: specimens and materials.- 4.5 Test procedure: frozen stress technique.- 4.6 Comparison of Hartranft-Sih theory with experiments.- References.- 5 Experimental determination of dynamic stress intensity factors by shadow patterns.- 5.1 Introduction.- 5.2 Physical and mathematical principles of the method.- 5.3 Theoretical analysis of the shadow pattern after Manogg: Mode-I-loaded stationary crack.- 5.4 Validity of the analysis for stationary cracks under dynamic loading.- 5.5 The dynamic correction for propagating cracks.- 5.6 Experimental technique and evaluation procedure.- 5.7 Applications.- 5.8 Concluding remarks.- References.- 6 Experimental determination of stress intensity factor by COD measurements.- 6.1 Introduction.- 6.2 Principle of the interference optical technique.- 6.3 Determination of stress intensity factor from crack opening displacement.- 6.4 Conclusion.- References.- Author’s Index.

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Book SynopsisWhen asked to start teaching a course on engineering fracture mechanics, I realized that a concise textbook, giving a general oversight of the field, did not exist. The explanation is undoubtedly that the subject is still in a stage of early development, and that the methodologies have still a very limited applicability. It is not possible to give rules for general application of fracture mechanics concepts. Yet our comprehension of cracking and fracture beha viour of materials and structures is steadily increasing. Further developments may be expected in the not too distant future, enabling useful prediction of fracture safety and fracture characteristics on the basis of advanced fracture mechanics procedures. The user of such advanced procedures m\lst have a general understanding of the elementary concepts, which are provided by this volume. Emphasis was placed on the practical application of fracture mechanics, but it was aimed to treat the subject in a way that may interest both metallurgists and engineers. For the latter, some general knowledge of fracture mechanisms and fracture criteria is indispensable for an apprecia­ tion of the limita tions of fracture mechanics. Therefore a general discussion is provided on fracture mechanisms, fracture criteria, and other metal­ lurgical aspects, without going into much detail. Numerous references are provided to enable a more detailed study of these subjects which are still in a stage of speculative treatment.Table of ContentsI Principles.- 1 Summary of basic problems and concepts.- 1.1 Introduction.- 1.2 A crack in a structure.- 1.3 The stress at a crack tip.- 1.4 The Griffith criterion.- 1.5 The crack opening displacement criterion.- 1.6 Crack propagation.- 1.7 Closure.- 2 Mechanisms of fracture and crack growth.- 2.1 Introduction.- 2.2 Cleavage fracture.- 2.3 Ductile fracture.- 2.4 Fatigue cracking.- 2.5 Environment assisted cracking.- 2.6 Service failure analysis.- 3 The elastic crack-tip stress field.- 3.1 The Airy stress function.- 3.2 Complex stress functions.- 3.3 Solution to crack problems.- 3.4 The effect of finite size.- 3.5 Special cases.- 3.6 Elliptical cracks.- 3.7 Some useful expressions.- 4 The crack tip plastic zone.- 4.1 The Irwin plastic zone correction.- 4.2 The Dugdale approach.- 4.3 The shape of the plastic zone.- 4.4 Plane stress versus plane strain.- 4.5 Plastic constraint factor.- 4.6 The thickness effect.- 5 The energy principle.- 5.1 The energy release rate.- 5.2 The criterion for crack growth.- 5.3 The crack resistance (R curve).- 5.4 Compliance.- 5.5 The J integral.- 5.6 Tearing modulus.- 5.7 Stability.- 6 Dynamics and crack arrest.- 6.1 Crack speed and kinetic energy.- 6.2 The dynamic stress intensity and elastic energy release rate.- 6.3 Crack branching.- 6.4 The principles of crack arrest.- 6.5 Crack arrest in practice.- 6.6 Dynamic fracture toughness.- 7 Plane strain fracture toughness.- 7.1 The standard test.- 7.2 Size requirements.- 7.3 Non-linearity.- 7.4 Applicability.- 8 Plane stress and transitional behaviour.- 8.1 Introduction.- 8.2 An engineering concept of plane stress.- 8.3 The R curve concept.- 8.4 The thickness effect.- 8.5 Plane stress testing.- 8.6 Closure.- 9 Elastic-plastic fracture.- 9.1 Fracture beyond general yield.- 9.2 The crack tip opening displacement.- 9.3 The possible use of the CTOD criterion.- 9.4 Experimental determination of CTOd.- 9.5 Parameters affecting the critical CTOD.- 9.6 Limitations, fracture at general yield.- 9.7 Use of the J integral.- 9.8 Limitations of the J integral.- 9.9 Measurement of JIc and JR.- 9.10 Closure.- 10 Fatigue crack propagation.- 10.1 Introduction.- 10.2 Crack growth and the stress intensity factor.- 10.3 Factors affecting crack propagation.- 10.4 Variable amplitude service loading.- 10.5 Retardation models.- 10.6 Similitude.- 10.7 Small cracks.- 10.8 Closure.- 11 Fracture resistance of materials.- 11.1 Fracture criteria.- 11.2 Fatigue cracking criteria.- 11.3 The effect of alloying and second phase particles.- 11.4 Effect of processing, anisotropy.- 11.5 Effect of temperature.- 11.6 Closure.- II Applications.- 12 Fail-safety and damage tolerance.- 12.1 Introduction.- 12.2 Means to provide fail-safety.- 12.3 Required information for fracture mechanics approach.- 12.4 Closure.- 13 Determination of stress intensity factors.- 13.1 Introduction.- 13.2 Analytical and numerical methods.- 13.3 Finite element methods.- 13.4 Experimental methods.- 14 Practical problems.- 14.1 Introduction.- 14.2 Through cracks emanating from holes.- 14.3 Corner cracks at holes.- 14.4 Cracks approaching holes.- 14.5 Combined loading.- 14.6 Fatigue crack growth under mixed mode loading.- 14.7 Biaxial loading.- 14.8 Fracture toughness of weldments.- 14.9 Service failure analysis.- 15 Fracture of structures.- 15.1 Introduction.- 15.2 Pressure vessels and pipelines.- 15.3 “Leak-bcfore-break” criterion.- 15.4 Material selection.- 15.5 The use of the J integral for structural analysis.- 15.6 Collapse analysis.- 15.7 Accuracy of fracture calculations.- 16 Stiffened sheet structures.- 16.1 Introduction.- 16.2 Analysis.- 16.3 Fatigue crack propagation.- 16.4 Residual strength.- 16.5 The R curve and the residual strength of stiffened panels.- 16.6 Other analysis methods.- 16.7 Crack arrest.- 16.8 Closure.- 17 Prediction of fatigue crack growth.- 17.1 Introduction.- 17.2 The load spectrum.- 17.3 Approximation of the stress spectrum.- 17.4 Generation of a stress history.- 17.5 Crack growth integration.- 17.6 Accuracy of predictions.- 17.7 Safety factors.- Author index.

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Book SynopsisOne studying the motion of fluids relative to particulate systems is soon impressed by the dichotomy which exists between books covering theoretical and practical aspects. Classical hydrodynamics is largely concerned with perfect fluids which unfortunately exert no forces on the particles past which they move. Practical approaches to subjects like fluidization, sedimentation, and flow through porous media abound in much useful but uncorrelated empirical information. The present book represents an attempt to bridge this gap by providing at least the beginnings of a rational approach to fluid­ particle dynamics, based on first principles. From the pedagogic viewpoint it seems worthwhile to show that the Navier-Stokes equations, which form the basis of all systematic texts, can be employed for useful practical applications beyond the elementary problems of laminar flow in pipes and Stokes law for the motion of a single particle. Although a suspension may often be viewed as a continuum for practical purposes, it really consists of a discrete collection of particles immersed in an essentially continuous fluid. Consideration of the actual detailed boundary­ value problems posed by this viewpoint may serve to call attention to the limitation of idealizations which apply to the overall transport properties of a mixture of fluid and solid particles.Table of Contents1. Introduction.- 1–1 Definition and purpose, 1. 1–2 Historical review, 8. 1–3 Application in science and technology, 13..- 2. The Behavior of Fluids in Slow Motion.- 2–1 The equations of change for a viscous fluid, 23. 2–2 Mechanical energy dissipation in a viscous fluid, 29. 2–3 Force and couple acting on a body moving in a viscous fluid, 30. 2–4 Exact solutions of the equations of motion for a viscous fluid, 31. 2–5 Laminar flow in ducts, 33. 2–6 Simplifications of the Navier-Stokes equations, especially for slow motion, 40. 2–7 Paradoxes in the solution of the creeping motion equations, 47. 2–8 Molecular effects in fluid dynamics, 49. 2–9 Non-newtonian flow, 51. 2–10 Unsteady creeping flows, 52..- 3. Some General Solutions and Theorems Pertaining to the Creeping Motion Equations.- 3–1 Introduction, 58. 3–2 Spherical coordinates, 62. 3–3 Cylindrical coordinates, 71. 3–4 Integral representations, 79. 3–5 Generalized reciprocal theorem, 85. 3–6 Energy dissipation, 88..- 4. Axisymmetrical Flow.- 4–1 Introduction, 96. 4–2 Stream function, 96. 4–3 Relation between stream function and local velocity, 98. 4–4 Stream function in various coordinate systems, 99. 4–5 Intrinsic coordinates, 100. 4–6 Properties of the stream function, 102. 4–7 Dynamic equation satisfied by the stream function, 103. 4–8 Uniform flow, 106. 4–9 Point source or sink, 106. 4–10 Source and sink of equal strength, 107. 4–11 Finite line source, 108. 4–12 Point force, 110. 4–13 Boundary conditions satisfied by the stream function, 111. 4–14 Drag on a body, 113. 4–15 Pressure, 116. 4–16 Separable coordinate systems, 117. 4–17 Translation of a sphere, 119. 4–18 Flow past a sphere, 123. 4–19 Terminal settling velocity, 124. 4–20 Slip at the surface of a sphere, 125. 4–21 Fluid sphere, 127. 4–22 Concentric spheres, 130. 4–23 General solution in spherical coordinates, 133. 4–24 Flow through a conical diffuser, 138. 4–25 Flow past an approximate sphere, 141. 4–26 Oblate spheroid, 145. 4–27 Circular disk, 149. 4–28 Flow in a venturi tube, 150. 4–29 Flow through a circular aperture, 153. 4–30 Prolate spheroid, 154. 4–31 Elongated rod, 156. 4–32 Axisymmetric flow past a spherical cap, 157..- 5. The Motion of a Rigid Particle of Arbitrary Shape in an Unbounded Fluid.- 5–1. Introduction, 159. 5–2 Translational motions, 163. 5–3 Rotational motions, 169. 5–4 Combined translation and rotation, 173. 5–5 Symmetrical particles, 183. 5–6 Nonskew bodies, 192. 5–7 Terminal settling velocity of an arbitrary particle, 197. 5–8 Average resistance to translation, 205. 5–9 The resistance of a slightly deformed sphere, 207. 5–10 The settling of spherically isotropic bodies, 219. 5–11 The settling of orthotopic bodies, 220..- 6. Interaction between Two or More Particles.- 6–1 Introduction, 235. 6–2 Two widely spaced spherically isotropic particles, 240: 6–3 Two spheres by the method of reflections and similar techniques, 249. 6–4 Exact solution for two spheres falling along their line of centers, 270. 6–5 Comparison of theories with experimental data for two spheres, 273. 6–6 More than two spheres, 276. 6–7 Two spheroids in a viscous liquid, 278. 6–8 Limitations of creeping motion equations, 281..- 7. Wall Effects on the Motion of a Single Particle.- 7–1 Introduction, 286. 7–2 The translation of a particle in proximity to container walls, 288. 7–3 Sphere moving in an axial direction in a circular cylindrical tube, 298. 7–4 Sphere moving relative to plane walls, 322. 7–5 Spheroid moving relative to cylindrical and plane walls, 331. 7–6 k-coefficients for typical boundaries, 340. 7–7 One- and two-dimensional problems, 341. 7–8 Solid of revolution rotating symmetrically in a bounded fluid, 346. 7–9 Unsteady motion of a sphere in the presence of a plane wall, 354..- 8. Flow Relative to Assemblages of Particles.- 8–1 Introduction, 358. 8–2 Dilute systems—no interaction effects, 360. 8–3 Dilute systems—first-order interaction effects, 371. 8–4 Concentrated systems, 387. 8–5 Systems with complex geometry, 400. 8–6 Particulate suspensions, 410. 8–7 Packed beds, 417. 8–8 Fluidization, 422..- 9. The Viscosity of Particulate Systems.- 9–1 Introduction, 431. 9–2 Dilute systems of spheres—no interaction effects, 438. 9–3 Dilute systems—first-order interaction effects, 443. 9–4 Concentrated systems, 448. 9–5 Nonspherical and nonrigid particles, 456. 9–6 Comparison with data, 462. 9–7 Non-newtonian behavior, 469..- Appendix A. Orthogonal Curvilinear Coordinate Systems.- A-l Curvilinear coordinates, 474. A-2 Orthogonal curvilinear coordinates, 477. A-3 Geometrical properties, 480. A-4 Differentiation of unit vectors, 481. A-5 Vector differential invariants, 483. A-6 Relations between cartesian and orthogonal curvilinear coordinates, 486. A-7 Dyadics in orthogonal curvilinear coordinates, 488. A-8 Cylindrical coordinate systems, 490. A-9 Circular cylindrical coordinates, 490. A-10 Conjugate cylindrical coordinate systems, 494. A-ll Elliptic cylinder coordinates, 495. A-12 Bipolar cylinder coordinates, 497. A-l3 Parabolic cylinder coordinates, 500. A-14 Coordinate systems of revolution, 501. A-l5 Spherical Coordinates, 504. A-l6 Conjugate coordinate systems of revolution, 508. A-17 Prolate spheroidal coordinates, 509. A-18 Oblate spheroidal coordinates, 512. A-19 Bipolar coordinates, 516. A-20 Toroidal coordinates, 519. A-21 Paraboloidal Coordinates, 521..- Appendix B. Summary of Notation and Brief Review of Polyadic Algebra.- Name Index.

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Book SynopsisThis book stems from a course on Micromechanics that I started about fifteen years ago at Northwestern University. At that time, micromechanics was a rather unfamiliar subject. Although I repeated the course every year, I was never convinced that my notes have quite developed into a final manuscript because new topics emerged constantly requiring revisions, and additions. I finally came to realize that if this is continued, then I will never complete the book to my total satisfaction. Meanwhile, T. Mori and I had coauthored a book in Japanese, entitled Micromechanics, published by Baifu-kan, Tokyo, in 1975. It received an extremely favorable response from students and re­ searchers in Japan. This encouraged me to go ahead and publish my course notes in their latest version, as this book, which contains further development of the subject and is more comprehensive than the one published in Japanese. Micromechanics encompasses mechanics related to microstructures of materials. The method employed is a continuum theory of elasticity yet its applications cover a broad area relating to the mechanical behavior of materi­ als: plasticity, fracture and fatigue, constitutive equations, composite materi­ als, polycrystals, etc. These subjects are treated in this book by means of a powerful and unified method which is called the 'eigenstrain method. ' In particular, problems relating to inclusions and dislocations are most effectively analyzed by this method, and therefore, special emphasis is placed on these topics.Trade Review`Professor Mura's book may be heartily recommended to those interested in either applying or learning to apply the methods of continuum mechanics to treat defects in the solid state. This monograph could serve as the perfect text for a second-level graduate course with the same title as that of the book.' Journal of Applied Mechanics Table of Contents1. General theory of eigenstrains.- 1. Definition of eigenstrains.- 2. Fundamental equations of elasticity.- Hooke’s law.- Equilibrium conditions.- Compatibility conditions.- 3. General expressions of elastic fields for given eigenstrain distributions.- Periodic solutions.- Method of Fourier series and Fourier integrals.- Method of Green’s functions.- Isotropic materials.- Cubic crystals.- Hexagonal crystals (transversely isotropic).- 4. Exercises of general formulae.- A straight screw dislocation.- A straight edge dislocation.- Periodic distribution of cuboidal precipitates.- 5. Static Green’s functions.- Isotropic materials.- Anisotropic materials.- Transversely isotropic materials.- Kröner’s formula.- Derivatives of Green’s functions.- Two-dimensional Green’s function.- 6. Inclusions and inhomogeneities.- Inclusions.- Inhomogeneities.- Effect of isotropic elastic moduli on stress.- 7. Dislocations.- Volterra and Mura formulas.- The Indenbom and Orlov formula.- Disclinations.- 8. Dynamic solutions.- Uniformly moving edge dislocation.- Uniformly moving screw dislocation.- 9. Dynamic Green’s functions.- Isotropic materials.- Steady State.- 10. Incompatibility.- Riemann-Christoffel curvature tensor.- 2. Isotropic inclusions.- 11. Eshelby’s solution.- Interior points.- Sphere.- Elliptic cylinder.- Penny-shape.- Flat ellipsoid.- Oblate spheroid.- Prolate spheroid.- Exterior points.- Thermal expansion with central symmetry.- 12. Ellipsoidal inclusions with polynomial eigenstrains.- The I-integrals.- Sphere.- Elliptic cylinder.- Oblate spheroid.- Prolate spheroid.- Elliptical plate.- The Ferrers and Dyson formula.- 13. Energies of inclusions.- Elastic strain energy.- Interaction energy.- Strain energy due to a spherical inclusion.- Elliptic cylinder.- Penny-shaped flat ellipsoid.- Spheroid.- 14. Cuboidal inclusions.- 15. Inclusions in a half space.- Green’s functions.- Ellipsoidal inclusion with a uniform dilatational eigenstrain.- Cuboidal inclusion with uniform eigenstrains.- Periodic distribution of eigenstrains.- Joined half-spaces.- 3. Anisotropic inclusions.- 16. Elastic field of an ellipsoidal inclusion.- 17. Formulae for interior points.- Uniform eigenstrains.- Spheroid.- Cylinder (elliptic inclusion).- Flat ellipsoid.- Eigenstrains with polynomial variation.- Eigenstrains with a periodic form.- 18. Formulae for exterior points.- Examples.- 19. Ellipsoidal inclusions with polynomial eigenstrains in anisotropic media.- Special cases.- 20. Harmonic eigenstrains.- 21. Periodic distribution of spherical inclusions.- 4. Ellipsoidal inhomogeneities.- 22. Equivalent inclusion method.- Isotropic materials.- Sphere.- Penny shape.- Rod.- Anisotropic inhomogeneities in isotropic matrices.- Stress field for exterior points.- 23. Numerical calculations.- Two ellipsoidal inhomogeneities.- 24. Impotent eigenstrains.- 25. Energies of inhomogeneities.- Elastic strain energy.- Interaction energy.- Colunneti’s theorem.- Uniform plastic deformation in a matrix.- Energy balance.- 26. Precipitates and martensites.- Isotropic precipitates.- Anistropic precipitates.- Incoherent precipitates.- Martensitic transformation.- Stress orienting precipitation.- 5. Cracks.- 27. Critical stresses of crakes in isotropic media.- Penny-shaped cracks.- Slit-like cracks.- Flat ellipsoidal cracks.- Crack opening displacement.- 28. Critical stresses of cracks in anisotropic media.- Uniform applied stress.- Non-uniform applied stress.- II integrals for a penny-shaped crack.- II integrals for cubic crystals.- II integrals for transversely isotropic materials.- 29. Stress intensity factor for a flat ellipsoidal crack.- Uniform applied stresses.- Non-uniform applied stresses.- 30. Stress intensity factor for a slit-like crack.- Uniform applied stresses.- Non-uniform applied stresses.- Isotropic materials.- 31. Stress concentration factors.- Simple tension.- Pure shear.- 32. Dugdale-Barenblatt cracks.- BCS model.- Penny shaped crack.- 33. Stress intensity factor for an arbitrarily shaped plane crack.- Numerical examples.- 34. Crack growth.- Energy release rate.- The J-integral.- Fatigue.- Dynamic crack growth.- 6. Dislocations.- 35. Displacement fields.- Parallel dislocations.- A straight dislocation.- 36. Stress fields.- Dislocation segments.- Willis’ formula.- The Asaro et al. formula.- Dislocation loops.- 37. Dislocation density tensor.- Surface dislocation density.- Impotent distribution of dislocations.- 38. Dislocation flux tensor.- Line integral expression of displacement and plastic distortion fields.- The elastic field of moving dislocationswave equations of tensor potentials.- Wave equations of tensor potentials.- 39. Energies and forces.- Dynamic consideration.- 40. Plasticity.- Mathematical theory of plasticity.- Dislocation theory.- Plane strain problems.- Beams and cylinders.- 41. Dislocation model for fatigue crack initiation.- 7. Material properties and related topics.- 42. Macroscopic average.- Average of internal stresses.- Macroscopic strains.- Tanaka-Mori’s theorem.- Image stress.- Random distribution of inclusions-Mori and Tanaka’s theory.- 43. Work-hardening of dispersion hardened alloys.- Work-hardening in simple shear.- Dislocations around an inclusion.- Uniformity of plastic deformation.- 44. Diffusional relaxation of internal and external stresses.- Relaxation of the internal stress in a plastically deformed dispersion strenthened alloy.- Diffusional relaxation process, climb rate of an Orowan loop.- Recovery creep of a dispersion strengthened alloy.- Interfacial diffusional relaxation.- 45. Average elastic moduli of composite materials.- The Voigt approximation.- The Reuss approximation.- Hill’s theory.- Eshelby’s method.- Self-consistent method.- Upper and lower bounds.- Other related works.- 46. Plastic behavior of polycrystalline metals and composites.- Taylor’s analysis.- Self-consistent method.- Embedded weakened zone.- 47. Viscoelasticity of composite materials.- Homogeneous inclusions.- Inhomogeneous inclusions.- Waves in an infinite medium.- 48. Elastic wave scattering.- Dynamic equivalent inclusion method.- Green’s formula.- 49. Interaction between dislocations and inclusions.- Inclusions and dislocations.- Cracks in two-phase materials.- 50. Eigenstrains in lattice theory.- A uniformly moving screw dislocation.- 51. Sliding inclusions.- Shearing Eigenstrains.- Spheroidol inhomogeneous inclusions.- 52. Recent developments.- Inclusions, precipitates, and composites.- Half-spaces.- Non-elastic matrices.- Cracks and inclusions.- Sliding and debonding inclusions.- Dynamic cases.- Miscellaneous.- Appendix 1.- Einstein summation convention.- Kronecker delta.- Permutation tensor.- Appendix 2.- The elastic moduli for isotropic materials.- Appendix 3.- Fourier series and integrals.- Dirac’s delta function and Heaviside’s step function.- Laplace transform.- Appendix 4.- Dislocations pile-up.- References.- Author index.

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Book SynopsisThe aim of this work is to bridge the gap between the well-known Newtonian mechanics and the studies on chaos, ordinarily reserved to experts. Several topics are treated: Lagrangian, Hamiltonian and Jacobi formalisms, studies of integrable and quasi-integrable systems. The chapter devoted to chaos also enables a simple presentation of the KAM theorem. All the important notions are recalled in summaries of the lectures. They are illustrated by many original problems, stemming from real-life situations, the solutions of which are worked out in great detail for the benefit of the reader. This book will be of interest to undergraduate students as well as others whose work involves mechanics, physics and engineering in general.Trade ReviewFrom the reviews:“The present book fills an important gap in the scientific literature since most books on analytical mechanics concentrate on the theoretical aspects. A great number of exercises and problems are divided into eight chapters … . In conclusion, this is an excellent source of concrete examples for students and mathematicians from several fields.” (Mircea Crâşmăreanu, Zentralblatt MATH, Vol. 1172, 2009)Table of ContentsForeword Synoptic Tables. Chapter 1 : The Lagrangian formulation (1 1 problems) Chapter 2 : Lagrangian systems (14 problems) Chapter 3 : The Hamilton's principle (15 problems) Chapter 4 : The Hamiltonian formalism (17 problems) Chapter 5 : The Hamilton-Jacobi formalism (1 1 problems) Chapter 6 : Integrable systems (18 problems) Chapter 7 : Quasi-integrable systems (9 problems) Chapter 8 : From order to chaos (12 problems). Bibliography.

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Book SynopsisA groundbreaking work in the field of physics and mathematics. In this monumental work, Newton formulated the laws of motion and universal gravitation, laying the foundation for classical mechanics and revolutionizing our understanding of the physical world. The Principia remains one of the most significant scientific books ever written, influencing generations of scientists, and shaping the course of modern physics and mathematics. The Groundbreaking Work of Sir Isaac Newton Mathematical proofs and equations. Comprehensive coverage of planetary motion. Helps in understanding the principles of motion. Logical and rigorous approach to scientific inquiry. Studied and revered as a seminal work in the field of science.

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Book SynopsisThis publication is aimed at students, teachers, and researchers of Continuum Mechanics and focused extensively on stating and developing Initial Boundary Value equations used to solve physical problems. With respect to notation, the tensorial, indicial and Voigt notations have been used indiscriminately. The book is divided into twelve chapters with the following topics: Tensors, Continuum Kinematics, Stress, The Objectivity of Tensors, The Fundamental Equations of Continuum Mechanics, An Introduction to Constitutive Equations, Linear Elasticity, Hyperelasticity, Plasticity (small and large deformations), Thermoelasticity (small and large deformations), Damage Mechanics (small and large deformations), and An Introduction to Fluids. Moreover, the text is supplemented with over 280 figures, over 100 solved problems, and 130 references.Trade ReviewFrom the reviews:“The book is meant as a textbook for master and doctoral students and researchers. It is based on lecture notes of civil engineering courses of the author given at the University of Castillia-La Mancha (Spain). So the reader can expect a careful and detailed introduction to the subject without too much novelty. … The book is perhaps helpful for those readers who have already a strong background in continuum mechanics and want to find additional information on topics … .” (Albrecht Bertram, zbMATH, Vol. 1277, 2014)Table of ContentsPreface.- Abbreviations.- Operators And Symbols.- Si-Units.- Introduction.- 1 Mechanics.- 2 What Is Continuum Mechanics.- 3 Scales Of Material Studies.- 4 The Initial Boundary Value Problem (Ibvp).- 1 Tensors.- 1.1 Introduction.- 1.2 Algebraic Operations With Vectors.- 1.3 Coordinate Systems.- 1.4 Indicial Notation.- 1.5 Algebraic Operations With Tensors.- 1.6 The Tensor-Valued Tensor Function.- 1.7 The Voigt Notation.- 1.8 Tensor Fields.- 1.9 Theorems Involving Integrals.- Appendix A: A Graphical Representation Of A Second-Order Tensor.- A.1 Projecting A Second-Order Tensor Onto A Particular Direction.- A.2 Graphical Representation Of An Arbitrary Second-Order Tensor.- A.3 The Tensor Ellipsoid.- A.4 Graphical Representation Of The Spherical And Deviatoric Parts.- 2 Continuum Kinematics.- 2.1 Introduction.- 2.2 The Continuous Medium.- 2.3 Description Of Motion.- 2.4 The Material Time Derivative.- 2.5 The Deformation Gradient.- 2.6 Finite Strain Tensors.- 2.7 Particular Cases Of Motion.- 2.8 Polar Decomposition Of F.- 2.9 Area And Volume Elements Deformation.- 2.10 Material And Control Domains.- 2.11 Transport Equations.- 2.12 Circulation And Vorticity.- 2.13 Motion Decomposition: Volumetric And Isochoric Motions.- 2.14 The Small Deformation Regime.- 2.15 Other Ways To Define Strain.- 3 Stress.- 3.1 Introduction.- 3.2 Forces.- 3.3 Stress Tensors.- 4 Objectivity Of Tensors.- 4.1 Introduction.- 4.2 The Objectivity Of Tensors.- 4.3 Tensor Rates.- 5 The Fundamental Equations Of Continuum Mechanics.- 5.1 Introduction.- 5.2 Density.- 5.3 Flux.- 5.4 The Reynolds Transport Theorem.- 5.5 Conservation Law.- 5.6 The Principle Of Conservation Of Mass. The Mass Continuity Equation.- 5.7 The Principle Of Conservation Of Linear Momentum. The Equations Of Motion.- 5.8 The Principle Of Conservation Of Angular Momentum. Symmetry Of The Cauchy Stress Tensor.- 5.9 The Principle Of Conservation Of Energy. The Energy Equation.- 5.10 The Principle Of Irreversibility. Entropy Inequality.- 5.11 Fundamental Equations Of Continuum Mechanics.- 5.12 Flux Problems.- 5.13 Fluid Flow In Porous Media (Filtration).- 5.14 The Convection-Diffusion Equation.- 5.15 Initial Boundary Value Problem (Ibvp) And Computational Mechanics.- 6 Introduction To Constitutive Equations.- 6.1 Introduction.- 6.2 The Constitutive Principles.- 6.3 Characterization Of Constitutive Equations For Simple Thermoelastic Materials.- 6.4 Characterization Of The Constitutive Equations For A Thermoviscoelastic Material.- 6.5 Some Experimental Evidence.- 7 Linear Elasticity.- 7.1 Introduction.- 7.2 Initial Boundary Value Problem Of Linear Elasticity.- 7.3 Generalized Hooke’s Law.- 7.4 The Elasticity Tensor.- 7.5 Isotropic Materials.- 7.6 Strain Energy Density.- 7.7 The Constitutive Law For Orthotropic Material.- 7.8 Transversely Isotropic Materials.- 7.9 The Saint-Venant’s And Superposition Principles.- 7.10 Initial Stress/Strain.- 7.11 The Navier-Lamé Equations.- 7.12 Two-Dimensional Elasticity.- 7.13 The Unidimensional Approach.- 8 Hyperelasticity.- 8.1 Introduction.- 8.2 Constitutive Equations.- 8.3 Isotropic Hyperelastic Materials.- 8.4 Compressible Materials.- 8.5 Incompressible Materials.- 8.6 Examples Of Hyperelastic Models.- 8.7 Anisotropic Hyperelasticity.- 9 Plasticity.- 9.1 Introduction.- 9.2 The Yield Criterion.- 9.3 Plasticity Models In Small Deformation Regime (Uniaxial Cases).- 9.4 Plasticity In Small Deformation Regime (The Classical Plasticity Theory).- 9.5 Plastic Potential Theory.- 9.6 Plasticity In Large Deformation Regime.- 9.7 Large-Deformation Plasticity Based On The Multiplicative Decomposition Of The Deformation Gradient.- 10 Thermoelasticity.- 10.1 Thermodynamic Potentials.- 10.2 Thermomechanical Parameters.- 10.3 Linear Thermoelasticity.- 10.4 The Decoupled Thermo-Mechanical Problem In A Small Deformation Regime.- 10.5 The Classical Theory Of Thermoelasticity In Finite Strain (Large Deformation Regime).- 10.6 Thermoelasticity Based On The Multiplicative Decomposition Of The Deformation Gradient..- 10.7 Thermoplasticity In A Small Deformation Regime.- 11 Damage Mechanics.- 11.1 Introduction.- 11.2 The Isotropic Damage Model In A Small Deformation Regime.- 11.3 The Generalized Isotropic Damage Model.- 11.4 The Elastoplastic-Damage Model In A Small Deformation Regime.- 11.5 The Tensile-Compressive Plastic-Damage Model.- 11.6 Damage In A Large Deformation Regime.- 12 Introduction To Fluids.- 12.1 Introduction.- 12.2 Fluids At Rest And In Motion.- 12.3 Viscous And Non-Viscous Fluids.- 12.4 Laminar Turbulent Flow.- 12.5 Particular Cases.- 12.6 Newtonian Fluids.- 12.7 Stress, Dissipated And Recoverable Powers.- 12.8 The Fundamental Equations For Newtonian Fluids.- Bibliography.- Index.

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Book SynopsisThe aim of this work is to bridge the gap between the well-known Newtonian mechanics and the studies on chaos, ordinarily reserved to experts. Several topics are treated: Lagrangian, Hamiltonian and Jacobi formalisms, studies of integrable and quasi-integrable systems. The chapter devoted to chaos also enables a simple presentation of the KAM theorem. All the important notions are recalled in summaries of the lectures. They are illustrated by many original problems, stemming from real-life situations, the solutions of which are worked out in great detail for the benefit of the reader. This book will be of interest to undergraduate students as well as others whose work involves mechanics, physics and engineering in general.Trade ReviewFrom the reviews:“The present book fills an important gap in the scientific literature since most books on analytical mechanics concentrate on the theoretical aspects. A great number of exercises and problems are divided into eight chapters … . In conclusion, this is an excellent source of concrete examples for students and mathematicians from several fields.” (Mircea Crâşmăreanu, Zentralblatt MATH, Vol. 1172, 2009)Table of ContentsForeword Synoptic Tables. Chapter 1 : The Lagrangian formulation (1 1 problems) Chapter 2 : Lagrangian systems (14 problems) Chapter 3 : The Hamilton's principle (15 problems) Chapter 4 : The Hamiltonian formalism (17 problems) Chapter 5 : The Hamilton-Jacobi formalism (1 1 problems) Chapter 6 : Integrable systems (18 problems) Chapter 7 : Quasi-integrable systems (9 problems) Chapter 8 : From order to chaos (12 problems). Bibliography.

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Book SynopsisMicro Electro Mechanical Systems (MEMS) is already about a billion dollars a year industry and is growing rapidly. So far major emphasis has been placed on the fabrication processes for various devices. There are serious issues related to tribology, mechanics, surfacechemistry and materials science in the operationand manufacturingof many MEMS devices and these issues are preventing an even faster commercialization. Very little is understood about tribology and mechanical properties on micro- to nanoscales of the materials used in the construction of MEMS devices. The MEMS community needs to be exposed to the state-of-the-artoftribology and vice versa. Fundamental understanding of friction/stiction, wear and the role of surface contamination and environmental debris in micro devices is required. There are significantadhesion, friction and wear issues in manufacturing and actual use, facing the MEMS industry. Very little is understood about the tribology of bulk silicon and polysilicon films used in the construction ofthese microdevices. These issues are based on surface phenomenaand cannotbe scaled down linearly and these become increasingly important with the small size of the devices. Continuum theory breaks down in the analyses, e. g. in fluid flow of micro-scale devices. Mechanical properties ofpolysilicon and other films are not well characterized. Roughness optimization can help in tribological improvements. Monolayers of lubricants and other materials need to be developed for ultra-low friction and near zero wear. Hard coatings and ion implantation techniques hold promise.Table of ContentsPreface. 1. MEMS Fabrication Techniques. 2. MEMS Applications and Tribology Issues. 3. State-of-the-Art of Tribology: Macroscale Processes. 4. State-of-the-Art of Tribology: Micro- to Nanoscale Processes. 5. Tribology of MEMS Components and Materials. 6. Mechanical Property Measurements. 7. Modification and Characterization of Surfaces. 8. Breakout Sessions Report. 9. Panel Discussion Report. List of Participants. Subject Index. Editor's Vita.

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Book SynopsisThis book contains contributions from various authors on different important topics related with probabilistic methods used for the design of structures. Initially several of the papers were prepared for advanced courses on structural reliability or on probabilistic methods for structural design. These courses have been held in different countries and have been given by different groups of lecturers. They were aimed at engineers and researchers who already had some exposure to structural reliability methods and thus they presented overviews of the work in the various topics. The book includes a selection of those contributions, which can be of support for future courses or for engineers and researchers that want to have an update on specific topics. It is considered a complement to the existing textbooks on structural reliability, which normally ensure the coverage of the basic topics but then are not extensive enough to cover some more specialised aspects. In addition to the contributions drawn from those lectures there are several papers that have been prepared specifically for this book, aiming at complementing the others in providing an overall account of the recent advances in the field. It is with sadness that in the meanwhile we have seen the disappearance of two of the contributors to the book and, in fact two of the early contributors to this field.Trade Review`...The book is well-produced and the diagrams, tables and graphs are clearly readable. Structural engineers involved in stochastic design now have the opportunity to take advantage of this book.' The Structural Engineer, 78:19 (2000)Table of Contents1. Basic Concepts of Structural Design; J.F. Borges. 2. Quantification of Model Uncertainty; C. Guedes Soares. 3. Response Surface Methodology in Structural Reliability; L. Labeyrie. 4. Stochastic Modeling of Fatigue Crack Growth and Inspection; H.O. Madsen. 5. Probabilistic Fatigue Assessment of Welded Joints; N.K. Shetty. 6. Probabilistic Modelling of the Strength of Flat Compression Members; C. Guedes Soares. 7. Reliability Analysis with Implicit Formulations; J.P. Muzeau, M. Lemaire. 8. Methods of System Reliability in Multidimensional Spaces; R. Rackwitz. 9. Statistical Extremes as a Tool for Design; J. Tiago de Oliveira. 10. Stochastic Modelling of Load Combinations; H.O. Madsen. 11. Time-Variant Reliability for Non-Stationary Processes by the Outcrossing Approach; R. Rackwitz. 12. Simulation of Stochastic Processes and Fields to Model Loading and Material Uncertainties; G. Deodatis. 13. A Spectral Formulation of Stochastic Finite Elements; R.G. Ghanem, P.D. Spanos. 14. Stochastic Finite Elements via Response Surface: Fatigue Crack Growth Problems; P. Colombi, L. Faravelli. 15. Probability Based Structural Codes: Past and Future; J.F. Borges. 16. Reliability Based Seismic Design; F. Casciati, A. Callerio. 17. Risk Based Structural Maintenance Planning; M. Faber.

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Book SynopsisThis publication is aimed at students, teachers, and researchers of Continuum Mechanics and focused extensively on stating and developing Initial Boundary Value equations used to solve physical problems. With respect to notation, the tensorial, indicial and Voigt notations have been used indiscriminately. The book is divided into twelve chapters with the following topics: Tensors, Continuum Kinematics, Stress, The Objectivity of Tensors, The Fundamental Equations of Continuum Mechanics, An Introduction to Constitutive Equations, Linear Elasticity, Hyperelasticity, Plasticity (small and large deformations), Thermoelasticity (small and large deformations), Damage Mechanics (small and large deformations), and An Introduction to Fluids. Moreover, the text is supplemented with over 280 figures, over 100 solved problems, and 130 references.Trade ReviewFrom the reviews:“The book is meant as a textbook for master and doctoral students and researchers. It is based on lecture notes of civil engineering courses of the author given at the University of Castillia-La Mancha (Spain). So the reader can expect a careful and detailed introduction to the subject without too much novelty. … The book is perhaps helpful for those readers who have already a strong background in continuum mechanics and want to find additional information on topics … .” (Albrecht Bertram, zbMATH, Vol. 1277, 2014)Table of ContentsPreface.- Abbreviations.- Operators And Symbols.- Si-Units.- Introduction.- 1 Mechanics.- 2 What Is Continuum Mechanics.- 3 Scales Of Material Studies.- 4 The Initial Boundary Value Problem (Ibvp).- 1 Tensors.- 1.1 Introduction.- 1.2 Algebraic Operations With Vectors.- 1.3 Coordinate Systems.- 1.4 Indicial Notation.- 1.5 Algebraic Operations With Tensors.- 1.6 The Tensor-Valued Tensor Function.- 1.7 The Voigt Notation.- 1.8 Tensor Fields.- 1.9 Theorems Involving Integrals.- Appendix A: A Graphical Representation Of A Second-Order Tensor.- A.1 Projecting A Second-Order Tensor Onto A Particular Direction.- A.2 Graphical Representation Of An Arbitrary Second-Order Tensor.- A.3 The Tensor Ellipsoid.- A.4 Graphical Representation Of The Spherical And Deviatoric Parts.- 2 Continuum Kinematics.- 2.1 Introduction.- 2.2 The Continuous Medium.- 2.3 Description Of Motion.- 2.4 The Material Time Derivative.- 2.5 The Deformation Gradient.- 2.6 Finite Strain Tensors.- 2.7 Particular Cases Of Motion.- 2.8 Polar Decomposition Of F.- 2.9 Area And Volume Elements Deformation.- 2.10 Material And Control Domains.- 2.11 Transport Equations.- 2.12 Circulation And Vorticity.- 2.13 Motion Decomposition: Volumetric And Isochoric Motions.- 2.14 The Small Deformation Regime.- 2.15 Other Ways To Define Strain.- 3 Stress.- 3.1 Introduction.- 3.2 Forces.- 3.3 Stress Tensors.- 4 Objectivity Of Tensors.- 4.1 Introduction.- 4.2 The Objectivity Of Tensors.- 4.3 Tensor Rates.- 5 The Fundamental Equations Of Continuum Mechanics.- 5.1 Introduction.- 5.2 Density.- 5.3 Flux.- 5.4 The Reynolds Transport Theorem.- 5.5 Conservation Law.- 5.6 The Principle Of Conservation Of Mass. The Mass Continuity Equation.- 5.7 The Principle Of Conservation Of Linear Momentum. The Equations Of Motion.- 5.8 The Principle Of Conservation Of Angular Momentum. Symmetry Of The Cauchy Stress Tensor.- 5.9 The Principle Of Conservation Of Energy. The Energy Equation.- 5.10 The Principle Of Irreversibility. Entropy Inequality.- 5.11 Fundamental Equations Of Continuum Mechanics.- 5.12 Flux Problems.- 5.13 Fluid Flow In Porous Media (Filtration).- 5.14 The Convection-Diffusion Equation.- 5.15 Initial Boundary Value Problem (Ibvp) And Computational Mechanics.- 6 Introduction To Constitutive Equations.- 6.1 Introduction.- 6.2 The Constitutive Principles.- 6.3 Characterization Of Constitutive Equations For Simple Thermoelastic Materials.- 6.4 Characterization Of The Constitutive Equations For A Thermoviscoelastic Material.- 6.5 Some Experimental Evidence.- 7 Linear Elasticity.- 7.1 Introduction.- 7.2 Initial Boundary Value Problem Of Linear Elasticity.- 7.3 Generalized Hooke’s Law.- 7.4 The Elasticity Tensor.- 7.5 Isotropic Materials.- 7.6 Strain Energy Density.- 7.7 The Constitutive Law For Orthotropic Material.- 7.8 Transversely Isotropic Materials.- 7.9 The Saint-Venant’s And Superposition Principles.- 7.10 Initial Stress/Strain.- 7.11 The Navier-Lamé Equations.- 7.12 Two-Dimensional Elasticity.- 7.13 The Unidimensional Approach.- 8 Hyperelasticity.- 8.1 Introduction.- 8.2 Constitutive Equations.- 8.3 Isotropic Hyperelastic Materials.- 8.4 Compressible Materials.- 8.5 Incompressible Materials.- 8.6 Examples Of Hyperelastic Models.- 8.7 Anisotropic Hyperelasticity.- 9 Plasticity.- 9.1 Introduction.- 9.2 The Yield Criterion.- 9.3 Plasticity Models In Small Deformation Regime (Uniaxial Cases).- 9.4 Plasticity In Small Deformation Regime (The Classical Plasticity Theory).- 9.5 Plastic Potential Theory.- 9.6 Plasticity In Large Deformation Regime.- 9.7 Large-Deformation Plasticity Based On The Multiplicative Decomposition Of The Deformation Gradient.- 10 Thermoelasticity.- 10.1 Thermodynamic Potentials.- 10.2 Thermomechanical Parameters.- 10.3 Linear Thermoelasticity.- 10.4 The Decoupled Thermo-Mechanical Problem In A Small Deformation Regime.- 10.5 The Classical Theory Of Thermoelasticity In Finite Strain (Large Deformation Regime).- 10.6 Thermoelasticity Based On The Multiplicative Decomposition Of The Deformation Gradient..- 10.7 Thermoplasticity In A Small Deformation Regime.- 11 Damage Mechanics.- 11.1 Introduction.- 11.2 The Isotropic Damage Model In A Small Deformation Regime.- 11.3 The Generalized Isotropic Damage Model.- 11.4 The Elastoplastic-Damage Model In A Small Deformation Regime.- 11.5 The Tensile-Compressive Plastic-Damage Model.- 11.6 Damage In A Large Deformation Regime.- 12 Introduction To Fluids.- 12.1 Introduction.- 12.2 Fluids At Rest And In Motion.- 12.3 Viscous And Non-Viscous Fluids.- 12.4 Laminar Turbulent Flow.- 12.5 Particular Cases.- 12.6 Newtonian Fluids.- 12.7 Stress, Dissipated And Recoverable Powers.- 12.8 The Fundamental Equations For Newtonian Fluids.- Bibliography.- Index.

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Book SynopsisNow in its fully updated fourth edition, this leading text in its field is an exhaustive monograph on turbulence in fluids in its theoretical and applied aspects. The authors examine a number of advanced developments using mathematical spectral methods, direct-numerical simulations, and large-eddy simulations. The book remains a hugely important contribution to the literature on a topic of great importance for engineering and environmental applications, and presents a very detailed presentation of the field.Trade ReviewFrom the reviews of the fourth edition: "Turbulence in Fluids contains a wealth of information, and its author is a top-tier scientist. … The book is logically ordered and contains a comprehensive list of 738 references. … Lesieur’s monograph is recommended for those who already know quite a bit about turbulence, for the theoretically inclined, and in particular for those interested in homogeneous turbulence and geophysical flows and their numerical simulation." (Mohamed Gad-El-Hak, Siam Review, Vol. 51 (1), 2009)Table of Contentsto Turbulence in Fluid Mechanics.- Basic Fluid Dynamics.- Transition to Turbulence.- Shear Flow Turbulence.- Fourier Analysis of Homogeneous Turbulence.- Isotropic Turbulence: Phenomenology and Simulations.- Analytical Theories and Stochastic Models.- Two-Dimensional Turbulence.- Beyond Two-Dimensional Turbulence in GFD.- Statistical Thermodynamics of Turbulence.- Statistical Predictability Theory.- Large-Eddy Simulations.- Towards “Real World Turbulence”.

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Book SynopsisThe first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving the basic notions necessary to do research in several areas of mathematical physics connected with quantum mechanics, from solid state to singular interactions, many body theory, semi-classical analysis, quantum statistical mechanics. The structure of this book is suitable for a second-semester course, in which the lectures are meant to provide, in addition to theorems and proofs, an overview of a more specific subject and hints to the direction of research. In this respect and for the width of subjects this second volume differs from other monographs on Quantum Mechanics. The second volume can be useful for students who want to have a basic preparation for doing research and for instructors who may want to use it as a basis for the presentation of selected topics.Trade Review“QM has also been the source of many interesting mathematical problems and developments to which only very few books devote careful attention and discussion. One of the praiseworthy merits of Dell'Antonio's book is to present a comprehensive and updates account of such important mathematical results. … For these reasons the book qualifies as a must for the education of mathematical physics graduate students and clearly provides very useful information also for theoretical physicists as well for mathematicians.” (Franco Strocchi, zbMATH 1357.81001, 2017)“This is a huge book on the mathematical foundations of quantum theory, including both non-relativistic quantum mechanics (QM) and quantum field theories (QFT). … the specialized reader will find in the book a very nice reference for checking concepts and ways of proceedings in these domains. It is a remarkable book.” (Décio Krause, Mathematical Reviews, May, 2016)Table of ContentsElements of the history of Quantum Mechanics I.- Elements of the history of Quantum Mechanics II.- Axioms, states, observables, measurement, difficulties.- Entanglement, decoherence, Bell’s inequalities, alternative theories.- Automorphisms; Quantum dynamics; Theorems of Wigner, Kadison, Segal; Continuity andgenerators.- Operators on Hilbert spaces I; Basic elements.- Quadratic forms.- Properties of free motion, Anholonomy,Geometric phase.- Elements of C ∗-algebras, GNS representation,automorphisms and dynamical systems.- Derivations and generators. K.M.S. condition. Elements of modular structure. Standard form.- Semigroups and dissipations. Markov approximation.- Quantum dynamical semigroups I.- Positivity preserving contraction semigroups on C ∗-algebras.- Conditional expectations.- Complete Dissipations.- Weyl system, Weyl algebra, lifting symplectic maps.- Magnetic Weyl algebra.- A Theorem of Segal.- Representations of Bargmann, Segal, Fock.- Second quantization.- Other quantizations (deformation, geometric).

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Book SynopsisThis book takes the student from the Newtonian mechanics typically taught in the first and the second year to the areas of recent research. The discussion of topics such as invariance, Hamiltonian-Jacobi theory, and action-angle variables is especially complete; the last includes a discussion of the Hannay angle, not found in other texts. The final chapter is an introduction to the dynamics of nonlinear nondissipative systems. Connections with other areas of physics which the student is likely to be studying at the same time, such as electromagnetism and quantum mechanics, are made where possible. There is thus a discussion of electromagnetic field momentum and mechanical“hidden” momentum in the quasi-static interaction of an electric charge and a magnet. This discussion, among other things explains the“(e/c)A” term in the canonical momentum of a charged particle in an electromagnetic field. There is also a brief introduction to path integrals and their connection with Hamilton's principle, and the relation between the Hamilton-Jacobi equation of mechanics, the eikonal equation of optics, and the Schrödinger equation of quantum mechanics.The text contains 115 exercises. This text is suitable for a course in classical mechanics at the advanced undergraduate level.Table of ContentsNewton's laws; the principle of virtual work and D'Alembert's principle; Lagrange's equations; the principle of stationary action or Hamilton's principle; invariance transformations and constants of the motion; Hamilton's equations; canonical transformations; Hamilton-Jacobi theory; action-angle variables; non-integrable systems.

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Book SynopsisThis book is intended to serve as a text on dynamics for undergraduate students of engineering. The book provides in-depth discussions of the fundamentals of Newtonian mechanics, more commonly known as dynamics. Drawing on the author’s extensive experience in teaching the subject of dynamics at two Indian Institutes of Technology (IITs) and the Indian Institute of Engineering Science and Technology (IIEST), the book contains 498 line diagrams, 123 worked-out examples and 222 exercise problems. The answers to select exercise problems are provided at the end of the book. A wealth of detailed illustrations make the book ideally suited for both self self-study and classroom use at both introductory and secondary levels. Thus the book offers a valuable resource for both students and teachers of dynamics, addressing the main topics covered in core level courses on ‘Dynamics’ for students of civil, mechanical and aerospace engineering across the globe.Table of ContentsChapter 1: Introduction to the Science of Motion.- Chapter 2: Kinematics of Particles.- Chapter 3: Kinetics of Particles.- Chapter 4: Work and Energy.- Chapter 5: Impulse and Momentum.- Chapter 6: Dynamics of Rigid Bodies in Plane Motion.- Chapter 7: Special Topics.- Appendix: A.- Unit Multiplies.- Important Physical Quantities.- Moment of Inertia of Rigid Bodies.Appendix B: Answers to Exercise problems.

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Book SynopsisThis comprehensive volume presents a unified framework of continuum theories. It indicates that (i) microcontinuum theories (micromorphic and micropolar theories) are natural extension of classical continuum mechanics, and (ii) classical continuum mechanics is a special case of microcontinuum theories when the deformable material point is idealized as a single mathematical point. The kinematics and basic laws are rigorously derived. Based on axiomatic approach, constitutive theory is systematically derived for various kinds of materials, ranging from Stokesian fluid to thermo-visco-elastic-plastic solid. Material force and Thermomechanical-electromagnetic coupling are introduced and discussed. Moreover, general finite element methods for large-strain thermomechanical coupling physical phenomena are systematically formulated. Also, non-classical continuum theories (Nonlocal Theory, Mechanobiology, 4D printing, Poromechanics, and Non-Self-Similar Crack Propagation) are rigorously formulated with applications and demonstrated numerically.As an advanced monograph, this unique compendium can also be used as a textbook for several graduate courses, including continuum mechanics, finite element methods, and advanced engineering science theories. Extensive problems are provided to help students to better understand the topics covered.

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Book SynopsisThis book addresses a range of basic and essential topics, selected from the author's teaching and research activities, offering a comprehensive guide in three parts: Statics, Kinematics and Kinetics. Chapter 1 briefly discusses the history of classical and modern mechanics, while Chapter 2, presents preliminary knowledge, preparing readers for the subsequent chapters. Chapters 3 to 7 introduce statics, force analysis, simplification of force groups, equilibrium of the general coplanar force group, and the center of the parallel force group. The Kinematics section (Chapters 8 to 10), covers the motion of a particle, basic motion and planar motion of a rigid body.Lastly, the Kinetics section (Chapters 11 to 14) explores Newton’s law of motion, theorem of momentum, theorem of angular momentum, and theorem of kinetic energy. With numerous examples from engineering, illustrations, and step-by-step tutorials, the book is suitable for both classroom use and self-study. After completing the course, students will be able to simplify complex engineering structures and perform force and motion analyses on particles and structures, preparing them for further study and research. The book can be used as a textbook for undergraduate courses on fundamental aspects of theoretical mechanics, such as aerospace, mechanical engineering, petroleum engineering, automotive and civil engineering, as well as material science and engineering.Table of ContentsPreface.- Preliminary knowledge.- Fundamentals of statics.- Force analysis.- Simplification of a force group.- Equilibrium of the general coplanar force gruop.- Center of the parallel force group.- Motion of a particle.- Basic motion of the rigid body.- Planar motion of the rigid body.- Newton’s laws of motion.- Theorem of momentum.- Theorem of angular momentum.- Theorem of kinetic energy.- Summary.

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Book SynopsisThis textbook highlights the theory of fractional calculus and its wide applications in mechanics and engineering. It describes in details the research findings in using fractional calculus methods for modeling and numerical simulation of complex mechanical behavior. It covers the mathematical basis of fractional calculus, the relationship between fractal and fractional calculus, unconventional statistics and anomalous diffusion, typical applications of fractional calculus, and the numerical solution of the fractional differential equation. It also includes latest findings, such as variable order derivative, distributed order derivative and its applications. Different from other textbooks in this subject, the book avoids lengthy mathematical demonstrations, and presents the theories in close connection to the applications in an easily readable manner. This textbook is intended for students, researchers and professionals in applied physics, engineering mechanics, and applied mathematics. It is also of high reference value for those in environmental mechanics, geotechnical mechanics, biomechanics, and rheology.Table of ContentsPreface Chapter 1 Introduction 1.1 History of fractional calculus 1.2 Geometric and physical interpretation of fractional derivative equation 1.3 Application in science and engineering Chapter 2 Mathematical foundation of fractional calculus 2.1 Definition of fractional calculus 2.2 Properties of fractional calculus 2.3 Fourier and Laplace transform of the fractional calculus 2.4 Analytical solution of fractional-order equations 2.5 Questions and discussions Chapter 3 Fractal and fractional calculus 3.1 Fractal introduction and application 3.2 The relationship between fractional calculus and fractal Chapter 4 Fractional diffusion model 4.1 The fractional derivative anomalous diffusion equation 4.2 Statistical model of the acceleration distribution of turbulence particle 4.3 Lévy stable distributions 4.4 Stretched Gaussian distribution 4.5 Tsallis distribution 4.6 Ito formula 4.7 Random walk model Chapter 5 Typical applications of fractional differential equations 5.1 Power-law phenomena and non-gradient constitutive relation 5.2 Fractional Langevin equation 5.3 The complex damped vibration 5.4 Viscoelastic and rheological models 5.5 The power law frequency dependent acoustic dissipation 5.6 The fractional variational principle of mechanics 5.7 Fractional Schrödinger equation 5.8 Other application fields 5.9 Some applications of fractional calculus in biomechanics 5.10 Some applications of fractional calculus in the modeling of drug release process Chapter 6 Numerical methods for fractional differential equations 6.1 Time fractional differential equations 6.2 Space fractional differential equations 6.3 Open issues of numerical methods for FDEs Chapter 7 Current development and perspectives of fractional calculus 7.1 Summary and Discussion 7.2 Perspectives Appendix I Special Functions Appendix II Related electronic resources of fractional dynamics

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Book SynopsisThis textbook for courses in gas dynamics will be of interest to students and teachers in aerospace and mechanical engineering disciplines. It provides an in-depth explanation of compressible flows and ties together various concepts to build an understanding of the fundamentals of gas dynamics. The book is written in an easy to understand manner, with pedagogical aids such as chapter overviews, summaries, and descriptive and objective questions to help students evaluate their progress. The book contains example problems as well as end-of-chapter exercises. Detailed bibliographies are included at the end of each chapter to provide students with further resources. The book can be used as a core text in engineering coursework and also in professional development courses. Table of ContentsKinetic Theory of Gases and Fluid Properties.- Conservation Laws for Inviscid Flows.- Thermodynamics of Compressible Flows.- Propagation of Acoustic Wave.- Steady One-Dimensional Compressible Flows.- Normal Shock Waves.- Flow in Constant-Area Ducts with Friction.- Flow in Constant-Area Ducts with Heat Transfer.- Quasi-One-Dimensional Compressible Flows.- Oblique Shock and Expansion Waves.- Velocity Potential Equation for Compressible Flows.- Small Perturbation Theory.- Similarity Rules of Compressible Flows.- Method of Characteristics.

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Book SynopsisThis book offers an interdisciplinary theoretical approach based on non-equilibrium statistical thermodynamics and control theory for mathematically modeling shock-induced out-of-equilibrium processes in condensed matter. The book comprises two parts. The first half of the book establishes the theoretical approach, reviewing fundamentals of non-equilibrium statistical thermodynamics and control theory of adaptive systems. The latter half applies the presented approach to a problem on shock-induced plane wave propagation in condensed matter. The result successfully reproduces the observed feature of waveform propagation in experiments, which conventional continuous mechanics cannot access. Further, the consequent stress–strain relationships derived with relaxation and inertia effect in elastic–plastic transition determines material properties in transient regimes.Table of ContentsChapter 1 Models of continuum mechanics and their deficiencies 1.1 Description of macroscopic systems; macroscopic variables 1.2 Macroscopic transport equations 1.3 The problem of closure of the transport equations 1.4 Validity of continuum mechanics 1.5 Scale averaging effect on transport processes 1.6 Medium models and transient processes 1.7 The problem of a uniform description of the media motions 1.8 Deficiencies of the continuum mechanics concept 1.9 Short review of approaches to extension of continuum mechanics Chapter 2 Specific Features of Processes Far from Equilibrium 2.1 Experimental difficulties in studying non-equilibrium processes 2.2 Anomalous medium response to strong impact 2.3 The internal structure effects 2.4 Fluctuations, oscillations, instabilities 2.5 Multi-scale energy exchange between various degrees of freedom 2.6 Multi-stage relaxation processes 2.7 Finite speed of disturbances propagation and the delay effects 2.8 Influence of the loading duration and inertial effects 2.9 Dynamic self-organization of new internal structure in open systems 2.10 Predictive ability of modeling non-equilibrium processes Chapter 3 Macroscopic Description in Terms of Non-equilibrium Statistical Mechanics 3.1 Fundamentals of statistical mechanics 3.2 Description of macroscopic systems from the first principles 3.3 Main problem of non-equilibrium statistical mechanics 3.4 Rigorous statistical approaches to non-equilibrium processes 3.5 Non-equilibrium statistical operator by Zubarev 3.6 Bogolyubov’s hypothesis of attenuation of spatiotemporal correlations 3.7 The nonlocal thermodynamic relationships with memory between the conjugate macroscopic fluxes and gradients 3.8 Two type of the nonlocal effects 3.9 The disadvantages and new opportunities to close transport equations for high-rate processes Chapter 4 Thermodynamic Concepts Out of Equilibrium 4.1 Basic concepts and principles of thermodynamics 4.2 Linear thermodynamics of irreversible processes 4.3 Revision of the generally accepted thermodynamic concepts out of equilibrium 4.4 Local entropy production near and far from equilibrium 4.5 Total entropy generation and the second law of thermodynamics 4.6 Maximum entropy principle by Jaynes 4.7 Thermodynamic temporal evolution out of equilibrium 4.8 Influence of the constraints imposed on the system 4.9 Self-organization of new structures in thermodynamics Chapter 5 New Approach to Modeling Non-equilibrium Processes 5.1 Generalized constitutive relationships based on non-equilibrium statistical mechanics 5.2 Modeling spatiotemporal correlation functions 5.3 Temporal stages of the correlation attenuation 5.4 Deficiencies of the generally accepted models for the medium with complicated properties 5.5 Requirements to new approach to modeling shock-induced processes 5.6 Foundations of new approach to modeling transport processes far from equilibrium 5.7 New approach to modeling transport processes far from equilibrium 5.8 Distinctive features of new approach from semi-empirical models 5.9 Interrelationships between spatiotemporal correlations and dynamic structure of the system 5.10 Modeling correlation functions in boundary-value problems 5.11 Boundary conditions for nonlocal equations 5.12 The mathematical basis for the self-consistent problem formulation 5.13 Discrete size spectrum of the dynamic structure of a bounded system Chapter 6 Description of the Structure Evolution Using Methods of Control Theory of Adaptive Systems 6.1 Methods of control theory in physics. Cybernetical physics 6.2 Speed gradient principle by Fradkov for non-stationary complex systems 6.3 Description of the system temporal evolution at macroscale level 6.4 Temporal evolution of statistical distributions at microscale 6.5 The need to describe temporal evolution out of equilibrium at mesoscale 6.6 Principle of maximum entropy by Jaynes and the goal function of the structure evolution 6.7 Integral entropy production and reduction of irreversible losses due to self-organization 6.8 Internal control at mesoscale based on Speed gradient principle 6.9 Paths of the system evolution and prediction of the limit states 6.10 Influence of feedbacks on the paths of the system evolution Chapter 7 The Shock-Induced Planar Wave Propagation in Condensed Matter 7.1 Thermodynamic properties of solids 7.2 Wave processes in crystal lattice 7.3 Elastic properties of solids 7.4 Plastic deformation. Deficiencies of continuum mechanics 7.5 Shock wave as a non-equilibrium transient process 7.6 The integral model for the stress tensor without separation into elastic and plastic parts 7.7 Integral formulation of the problem of the shock-induced wave propagation in condensed matter 7.8 Self-similar quasi-stationary solution to the problem 7.9 The relaxation model of shock-induced waveforms during propagation 7.10 Comparison of the model waveforms with experimental data Chapter 8 Evolution of Waveforms during Propagation in Solids 8.1 Entropy production in finite-time waveforms 8.2 Speed gradient principle for the waveforms evolution 8.3 The waveform evolution during quasi-stationary wave propagation 8.4 Paths of the waveform evolution on a surface of the entropy production over a phase plane 8.5 Coincidence with experimental results Chapter 9 Abnormal Loss or Growth of the Wave Amplitude 9.1 Dependence of the waveform amplitude on the impact velocity 9.2 The wave amplitude loss due to various relaxation effects 9.3 Interference of shock wave at mesoscale 9.4 Wave packet spreading 9.5 Mass velocity dispersion and turbulent effects 9.6 Multi-scale momentum and energy exchange in wave processes 9.7 Self-organization and the structure instability Chapter 10 The Stress-Strain Relationships for the Continuous Stationary Loading 10.1 Difference between shock and continuous loading at the same amplitude 10.2 Influence of the relaxation and delay effects on the medium response to short and long loading 10.3 Entropy production surfaces for various duration loading and possible evolutionary paths 10.4 Meta-stable states and the system structural instability 10.5 Probable change of the evolution paths and their direction 10.6 Dependence of final states on the initial and loading conditions 10.7 Influence of the feedbacks between the structure evolution and the material response 10.8 Control of the evolution paths to obtain the desired structure of the material

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Book SynopsisThe book gives a general introduction to classical theoretical physics, in the fields of mechanics, relativity and electromagnetism. It is analytical in approach and detailed in the derivations of physical consequences from the fundamental principles in each of the fields. The book is aimed at physics students in the last year of their undergraduate or first year of their graduate studies.The text is illustrated with many figures, most of these in color. There are many useful examples and exercises which complement the derivations in the text.

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Book SynopsisThis book provides a general introduction to fluid mechanics in the form of biographies and popular science. Based on the author’s extensive teaching experience, it combines natural science and human history, knowledge inheritance and cognition law to replace abstract concepts of fluid mechanics with intuitive and understandable physical concepts. In seven chapters, it describes the development of fluid mechanics, aerodynamics, hydrodynamics, computational fluid dynamics, experimental fluid dynamics, wind tunnel and water tunnel equipment, the mystery of flight and aerodynamic principles, and leading figures in fluid mechanics in order to spark beginners’ interest and allow them to gain a comprehensive understanding of the field’s development. It also provides a list of references for further study.Table of ContentsFoundation of Fluid Mechanics.- Aerodynamics.- Hydrodynamics.- Computational Fluid Dynamics.- Experimental Fluid Mechanics.- Wind tunnel and water tunnel equipment.- Flight Mystery and Aerodynamic Principles.- Introduction to Celebrities in Fluid Mechanics.

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Book SynopsisMechanical systems with one degree of freedom.- Kepler's gravitational two-body problem.- Newtonian to Lagrangian and Hamiltonian mechanics.- Introduction to special relativistic mechanics.- Dynamics viewed as a vector ?eld on state space.- Small oscillations for one degree of freedom.- Nonlinear oscillations: pendulum and anharmonic oscillator.- Rigid body mechanics.- Motion in noninertial frames of reference.- Canonical transformations.- Angle-action variables.- Hamilton-Jacobi equation.- Normal modes of oscillation and linear stability.- Bifurcations: qualitative changes in dynamics.- From regular to chaotic motion.- Dynamics of continuous deformable media.- Vibrations of a stretched string and the wave equation.- Heat diffusion equation and Brownian motion.- Introduction to ?uid mechanics.

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Book SynopsisThis book describes the basic concepts and principles of classical mechanics in the intermediate level. Given the perspective thatdifferent mechanical problems require an appropriate approach drawn from various methods or principles, a textbook discussingmultiplemethods or principles in mechanics is highly desirable.Additionally, a good textbook should include historicalcontexton the motivation and the development of the methods or principles, allowing students to gain insights that may help them discover new theories. However, after many years of teaching Dynamics in the graduate school, the authorswere unable tofind a suitableintermediate-level textbook on classical mechanics, whichmotivated them to begin writing this book.For theaforementioned reasons, this book includes the descriptions of various methods or principles in mechanics, such as the Newton-Euler Principle, the d'Alembert Principle, Lagrangian methods, Gauss's Principle of Least Constraint, the Gibbs-Appell equation, Jourdain's equation, the Principle of Virtual Power, the Appell-Kane method, the Hamilton Principle, and the Hamiltonian mechanics, among others. Moreover, many historical remarks on the motivation and the development of the methods or principles are given in this book, as well asnumerousapplications. The authors also believe that instudyingthe motion of a material body, different models may be used depending on the application. If the position of the body is of interest, a particle model may be chosen. If the orientation or attitude of the body is under consideration, a rigid body model should be adopted. If deformation is a concern, a model of deformable body should be applied.Consequently,a book in mechanics for engineers should encompassa variety ofmodels of the body, ranging from particles to continua such as solids or fluids.This book also meets that need.

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Book SynopsisThis book highlights the pulchritudinous features of FRP composites emphasizing failure criteria referring to microstructural as well as micromechanical aspects. The potential and promises of this class of material as being explored for supercritical applications necessitate the analysis and assessment of FRPs with a spectrum of low to high strain rates. Additionally, constitutive modeling and shock properties of polymeric composites along with the data processing techniques and relevant theories for different characterization methods are conversed. The findings of previous studies available on mechanical characteristics of polymer composites under quasi-static and high-strain-rate circumstances are also discussed. The dearth of open literature and limited information culminate the need for this book which may eventually bridge the existing gap. Table of ContentsIntroduction to Composite Materials.- Polymer Matrix Materials for Ballistic Armors.- Fiber reinforcements.- Characterization techniques in different strain-rate spectrum.- Microstructural Failure Mechanisms Analysis.- Micromechanics of FRP Composites and the Analytical Approach for Ballistic Response.- Recent development of constitutive models for strain-rate sensitive FRP composite materials.- High-Velocity Impact Modeling in Materials Science: A Multiscale Perspective.- Interface Engineering.

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