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Mechanics of Solids and Materials

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Hardcover | 16 January 2006

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Hardcover
880 Pages

Dimensions(cm)
44 x 184 x 261

Hardcover

$294.75

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Mechanics of Solids and Materials intends to provide a modern and integrated treatment of the foundations of solid mechanics as applied to the mathematical description of material behavior. The 2006 book blends both innovative (large strain, strain rate, temperature, time dependent deformation and localized plastic deformation in crystalline solids, deformation of biological networks) and traditional (elastic theory of torsion, elastic beam and plate theories, contact mechanics) topics in a coherent theoretical framework. The extensive use of transform methods to generate solutions makes the book also of interest to structural, mechanical, and aerospace engineers. Plasticity theories, micromechanics, crystal plasticity, energetics of elastic systems, as well as an overall review of math and thermodynamics are also covered in the book.

Industry Reviews

"It is very comprehensive and goes into great depth in all the areas it covers...This is truly a work of scholarship." Brian Ralph, Materials Characterization

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You Can Find This Book In

Non-Fiction Engineering & Technology Technology in General Engineering in General Mechanical Engineering & Materials Materials Science Mechanics of Solids Science Physics Classical Mathematics Fluid Mechanics Electronics & Communications Engineering

Electronics Engineering Automatic Control Engineering Robotics

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Paperback

Published: 30th June 2011

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Preface	p. xix
Mathematical Preliminaries
Vectors and Tensors	p. 1
Vector Algebra	p. 1
Coordinate Transformation: Rotation of Axes	p. 4
Second-Rank Tensors	p. 5
Symmetric and Antisymmetric Tensors	p. 5
Prelude to Invariants of Tensors	p. 6
Inverse of a Tensor	p. 7
Additional Proofs	p. 7
Additional Lemmas for Vectors	p. 8
Coordinate Transformation of Tensors	p. 9
Some Identities with Indices	p. 10
Tensor Product	p. 10
Orthonormal Basis	p. 11
Eigenvectors and Eigenvalues	p. 12
Symmetric Tensors	p. 14
Positive Definiteness of a Tensor	p. 14
Antisymmetric Tensors	p. 15
Orthogonal Tensors	p. 17
Polar Decomposition Theorem	p. 19
Polar Decomposition: Physical Approach	p. 20
The Cayley-Hamilton Theorem	p. 22
Additional Lemmas for Tensors	p. 23
Identities and Relations Involving [down triangle, open] Operator	p. 23
Suggested Reading	p. 25
Basic Integral Theorems	p. 26
Gauss and Stokes's Theorems	p. 26
Vector and Tensor Fields: Physical Approach	p. 27
Surface Integrals: Gauss Law	p. 28
Evaluating Surface Integrals	p. 29
The Divergence	p. 31
Divergence Theorem: Relation of Surface to Volume Integrals	p. 33
More on Divergence Theorem	p. 34
Suggested Reading	p. 35
Fourier Series and Fourier Integrals	p. 36
Fourier Series	p. 36
Double Fourier Series	p. 37
Integral Transforms	p. 39
Dirichlet's Conditions	p. 42
Integral Theorems	p. 46
Convolution Integrals	p. 48
Fourier Transforms of Derivatives of f(x)	p. 49
Fourier Integrals as Limiting Cases of Fourier Series	p. 50
Dirac Delta Function	p. 51
Suggested Reading	p. 52
Continuum Mechanics
Kinematics of Continuum	p. 55
Preliminaries	p. 55
Uniaxial Strain	p. 56
Deformation Gradient	p. 57
Strain Tensor	p. 58
Stretch and Normal Strains	p. 60
Angle Change and Shear Strains	p. 60
Infinitesimal Strains	p. 61
Principal Stretches	p. 62
Eigenvectors and Eigenvalues of Deformation Tensors	p. 63
Volume Changes	p. 63
Area Changes	p. 64
Area Changes: Alternative Approach	p. 65
Simple Shear of a Thick Plate with a Central Hole	p. 66
Finite vs. Small Deformations	p. 68
Reference vs. Current Configuration	p. 69
Material Derivatives and Velocity	p. 71
Velocity Gradient	p. 71
Deformation Rate and Spin	p. 74
Rate of Stretching and Shearing	p. 75
Material Derivatives of Strain Tensors: E vs. D	p. 76
Rate of F in Terms of Principal Stretches	p. 78
Additional Connections Between Current and Reference State Representations	p. 82
Transport Formulae	p. 83
Material Derivatives of Volume, Area, and Surface Integrals: Transport Formulae Revisited	p. 84
Analysis of Simple Shearing	p. 85
Examples of Particle and Plane Motion	p. 87
Rigid Body Motions	p. 88
Behavior under Superposed Rotation	p. 89
Suggested Reading	p. 90
Kinetics of Continuum	p. 92
Traction Vector and Stress Tensor	p. 92
Equations of Equilibrium	p. 94
Balance of Angular Momentum: Symmetry of [sigma]	p. 95
Principal Values of Cauchy Stress	p. 96
Maximum Shear Stresses	p. 97
Nominal Stress	p. 98
Equilibrium in the Reference State	p. 99
Work Conjugate Connections	p. 100
Stress Deviator	p. 102
Frame Indifference	p. 102
Continuity Equation and Equations of Motion	p. 107
Stress Power	p. 108
The Principle of Virtual Work	p. 109
Generalized Clapeyron's Formula	p. 111
Suggested Reading	p. 111
Thermodynamics of Continuum	p. 113
First Law of Thermodynamics: Energy Equation	p. 113
Second Law of Thermodynamics: Clausius-Duhem Inequality	p. 114
Reversible Thermodynamics	p. 116
Thermodynamic Relationships with p, V, T, and s	p. 120
Theoretical Calculations of Heat Capacity	p. 123
Third Law of Thermodynamics	p. 125
Irreversible Thermodynamics	p. 127
Gibbs Conditions of Thermodynamic Equilibrium	p. 129
Linear Thermoelasticity	p. 130
Thermodynamic Potentials in Linear Thermoelasticity	p. 132
Uniaxial Loading and Thermoelastic Effect	p. 136
Thermodynamics of Open Systems: Chemical Potentials	p. 139
Gibbs-Duhem Equation	p. 141
Chemical Potentials for Binary Systems	p. 142
Configurational Entropy	p. 143
Ideal Solutions	p. 144
Regular Solutions for Binary Alloys	p. 145
Suggested Reading	p. 147
Nonlinear Elasticity	p. 148
Green Elasticity	p. 148
Isotropic Green Elasticity	p. 150
Constitutive Equations in Terms of B	p. 151
Constitutive Equations in Terms of Principal Stretches	p. 152
Incompressible Isotropic Elastic Materials	p. 153
Elastic Moduli Tensors	p. 153
Instantaneous Elastic Moduli	p. 155
Elastic Pseudomoduli	p. 155
Elastic Moduli of Isotropic Elasticity	p. 156
Elastic Moduli in Terms of Principal Stretches	p. 157
Suggested Reading	p. 158
Linear Elasticity
Governing Equations of Linear Elasticity	p. 161
Elementary Theory of Isotropic Linear Elasticity	p. 161
Elastic Energy in Linear Elasticity	p. 163
Restrictions on the Elastic Constants	p. 164
Compatibility Relations	p. 169
Compatibility Conditions: Cesaro Integrals	p. 170
Beltrami-Michell Compatibility Equations	p. 172
Navier Equations of Motion	p. 172
Uniqueness of Solution to Linear Elastic Boundary Value Problem	p. 174
Potential Energy and Variational Principle	p. 175
Betti's Theorem of Linear Elasticity	p. 177
Plane Strain	p. 178
Governing Equations of Plane Elasticity	p. 180
Thermal Distortion of a Simple Beam	p. 180
Suggested Reading	p. 182
Elastic Beam Problems	p. 184
A Simple 2D Beam Problem	p. 184
Polynomial Solutions to [down triangle, open superscript 4 phi] = 0	p. 185
A Simple Beam Problem Continued	p. 186
Beam Problems with Body Force Potentials	p. 188
Beam under Fourier Loading	p. 190
Complete Boundary Value Problems for Beams	p. 193
Suggested Reading	p. 198
Solutions in Polar Coordinates	p. 199
Polar Components of Stress and Strain	p. 199
Plate with Circular Hole	p. 201
Degenerate Cases of Solution in Polar Coordinates	p. 204
Curved Beams: Plane Stress	p. 206
Axisymmetric Deformations	p. 211
Suggested Reading	p. 213
Torsion and Bending of Prismatic Rods	p. 214
Torsion of Prismatic Rods	p. 214
Elastic Energy of Torsion	p. 216
Torsion of a Rod with Rectangular Cross Section	p. 217
Torsion of a Rod with Elliptical Cross Section	p. 221
Torsion of a Rod with Multiply Connected Cross Sections	p. 222
Bending of a Cantilever	p. 225
Elliptical Cross Section	p. 227
Suggested Reading	p. 228
Semi-Infinite Media	p. 229
Fourier Transform of Biharmonic Equation	p. 229
Loading on a Half-Plane	p. 230
Half-Plane Loading: Special Case	p. 232
Symmetric Half-Plane Loading	p. 234
Half-Plane Loading: Alternative Approach	p. 235
Additional Half-Plane Solutions	p. 237
Infinite Strip	p. 242
Suggested Reading	p. 245
Isotropic 3D Solutions	p. 246
Displacement-Based Equations of Equilibrium	p. 246
Boussinesq-Papkovitch Solutions	p. 247
Spherically Symmetrical Geometries	p. 248
Pressurized Sphere: Stress-Based Solution	p. 251
Spherical Indentation	p. 254
Point Forces on Elastic Half-Space	p. 261
Suggested Reading	p. 263
Anisotropic 3D Solutions	p. 264
Point Force	p. 264
Green's Function	p. 264
Isotropic Green's Function	p. 268
Suggested Reading	p. 270
Plane Contact Problems	p. 271
Wedge Problem	p. 271
Distributed Contact Forces	p. 274
Displacement-Based Contact: Rigid Flat Punch	p. 277
Suggested Reading	p. 279
Deformation of Plates	p. 280
Stresses and Strains of Bent Plates	p. 280
Energy of Bent Plates	p. 281
Equilibrium Equations for a Plate	p. 282
Shear Forces and Bending and Twisting Moments	p. 285
Examples of Plate Deformation	p. 287
Rectangular Plates	p. 289
Suggested Reading	p. 291
Micromechanics
Dislocations and Cracks: Elementary Treatment	p. 293
Dislocations	p. 293
Tensile Cracks	p. 295
Suggested Reading	p. 298
Dislocations in Anisotropic Media	p. 299
Dislocation Character and Geometry	p. 299
Dislocations in Isotropic Media	p. 302
Planar Geometric Theorem	p. 305
Applications of the Planar Geometric Theorem	p. 308
A 3D Geometrical Theorem	p. 312
Suggested Reading	p. 314
Cracks in Anisotropic Media	p. 315
Dislocation Mechanics: Reviewed	p. 315
Freely Slipping Crack	p. 316
Crack Extension Force	p. 319
Crack Faces Loaded by Tractions	p. 320
Stress Intensity Factors and Crack Extension Force	p. 322
Crack Tip Opening Displacement	p. 325
Dislocation Energy Factor Matrix	p. 325
Inversion of a Singular Integral Equation	p. 328
2D Anisotropic Elasticity - Stroh Formalism	p. 329
Suggested Reading	p. 334
The Inclusion Problem	p. 335
The Problem	p. 335
Eshelby's Solution Setup	p. 336
Calculation of the Constrained Fields: u[superscript c], e[superscript c], and [sigma superscript c]	p. 338
Components of the Eshelby Tensor for Ellipsoidal Inclusion	p. 341
Elastic Energy of an Inclusion	p. 343
Inhomogeneous Inclusion: Uniform Transformation Strain	p. 343
Nonuniform Transformation Strain Inclusion Problem	p. 345
Inclusions in Isotropic Media	p. 350
Suggested Reading	p. 354
Forces and Energy in Elastic Systems	p. 355
Free Energy and Mechanical Potential Energy	p. 355
Forces of Translation	p. 357
Interaction Between Defects and Loading Mechanisms	p. 362
Elastic Energy of a Dislocation	p. 366
In-Plane Stresses of Straight Dislocation Lines	p. 367
Chemical Potential	p. 369
Applications of the J Integral	p. 372
Suggested Reading	p. 374
Micropolar Elasticity	p. 375
Introduction	p. 375
Basic Equations of Couple-Stress Elasticity	p. 376
Displacement Equations of Equilibrium	p. 377
Correspondence Theorem of Couple-Stress Elasticity	p. 378
Plane Strain Problems of Couple-Stress Elasticity	p. 379
Edge Dislocation in Couple-Stress Elasticity	p. 381
Edge Dislocation in a Hollow Cylinder	p. 384
Governing Equations for Antiplane Strain	p. 386
Antiplane Shear of Circular Annulus	p. 390
Screw Dislocation in Couple-Stress Elasticity	p. 391
Configurational Forces in Couple-Stress Elasticity	p. 392
Energy-Momentum Tensor of a Couple-Stress Field	p. 396
Basic Equations of Micropolar Elasticity	p. 398
Noether's Theorem of Micropolar Elasticity	p. 400
Conservation Integrals in Micropolar Elasticity	p. 403
Conservation Laws for Plane Strain Micropolar Elasticity	p. 404
M Integral of Micropolar Elasticity	p. 404
Suggested Reading	p. 406
Thin Films and Interfaces
Dislocations in Bimaterials	p. 407
Introduction	p. 407
Screw Dislocation Near a Bimaterial Interface	p. 407
Edge Dislocation (b[subscript x]) Near a Bimaterial Interface	p. 410
Edge Dislocation (b[subscript y]) Near a Bimaterial Interface	p. 419
Strain Energy of a Dislocation Near a Bimaterial Interface	p. 423
Suggested Reading	p. 427
Strain Relaxation in Thin Films	p. 428
Dislocation Array Beneath the Free Surface	p. 428
Energy of a Dislocation Array	p. 430
Strained-Layer Epitaxy	p. 431
Conditions for Dislocation Array Formation	p. 432
Frank and van der Merwe Energy Criterion	p. 434
Gradual Strain Relaxation	p. 436
Stability of Array Configurations	p. 439
Stronger Stability Criteria	p. 439
Further Stability Bounds	p. 441
Suggested Reading	p. 446
Stability of Planar Interfaces	p. 447
Stressed Surface Problem	p. 447
Chemical Potential	p. 449
Surface Diffusion and Interface Stability	p. 450
Volume Diffusion and Interface Stability	p. 451
2D Surface Profiles and Surface Stability	p. 455
Asymptotic Stresses for 1D Surface Profiles	p. 457
Suggested Reading	p. 459
Plasticity and Viscoplasticity
Phenomenological Plasticity	p. 461
Yield Criteria for Multiaxial Stress States	p. 462
Von Mises Yield Criterion	p. 463
Tresca Yield Criterion	p. 465
Mohr-Coulomb Yield Criterion	p. 467
Gurson Yield Criterion for Porous Metals	p. 470
Anisotropic Yield Criteria	p. 470
Elastic-Plastic Constitutive Equations	p. 471
Isotropic Hardening	p. 473
Kinematic Hardening	p. 475
Constitutive Equations for Pressure-Dependent Plasticity	p. 478
Nonassociative Plasticity	p. 480
Plastic Potential for Geomaterials	p. 480
Rate-Dependent Plasticity	p. 482
Deformation Theory of Plasticity	p. 484
J[subscript 2] Corner Theory	p. 487
Rate-Dependent Flow Theory	p. 489
Elastic and Plastic Constitutive Contributions	p. 491
A Rate Tangent Integration	p. 493
Plastic Void Growth	p. 495
Suggested Reading	p. 501
Micromechanics of Crystallographic Slip	p. 502
Early Observations	p. 502
Dislocations	p. 508
Other Strengthening Mechanisms	p. 517
Measurements of Latent Hardening	p. 519
Observations of Slip in Single Crystals and Polycrystals at Modest Strains	p. 523
Deformation Mechanisms in Nanocrystalline Grains	p. 525
Suggested Reading	p. 537
Crystal Plasticity	p. 538
Basic Kinematics	p. 538
Stress and Stress Rates	p. 541
Convected Elasticity	p. 545
Rate-Dependent Slip	p. 547
Crystalline Component Forms	p. 550
Suggested Reading	p. 555
The Nature of Crystalline Deformation: Localized Plastic Deformation	p. 557
Perspectives on Nonuniform and Localized Plastic Flow	p. 557
Localized Deformation in Single Slip	p. 560
Localization in Multiple Slip	p. 576
Numerical Results for Crystalline Deformation	p. 580
Suggested Reading	p. 584
Polycrystal Plasticity	p. 586
Perspectives on Polycrystalline Modeling and Texture Development	p. 586
Polycrystal Model	p. 588
Extended Taylor Model	p. 590
Model Calculational Procedure	p. 592
Deformation Theories and Path-Dependent Response	p. 596
Suggested Reading	p. 600
Laminate Plasticity	p. 601
Laminate Model	p. 601
Additional Kinematical Perspective	p. 604
Final Constitutive Forms	p. 604
Suggested Reading	p. 607
Biomechanics
Mechanics of a Growing Mass	p. 609
Introduction	p. 609
Continuity Equation	p. 610
Reynolds Transport Theorem	p. 612
Momentum Principles	p. 614
Energy Equation	p. 615
Entropy Equation	p. 617
General Constitutive Framework	p. 619
Multiplicative Decomposition of Deformation Gradient	p. 622
Density Expressions	p. 624
Elastic Stress Response	p. 625
Partition of the Rate of Deformation	p. 626
Elastic Moduli Tensor	p. 627
Elastic Strain Energy Representation	p. 629
Evolution Equation for Stretch Ratio	p. 630
Suggested Reading	p. 631
Constitutive Relations for Membranes	p. 633
Biological Membranes	p. 633
Membrane Kinematics	p. 634
Constitutive Laws for Membranes	p. 637
Limited Area Compressibility	p. 638
Simple Triangular Networks	p. 639
Suggested Reading	p. 640
Solved Problems
Solved Problems for Chapters 1-33	p. 641
Bibliography	p. 833
Index	p. 853
Table of Contents provided by Ingram. All Rights Reserved.

Mechanics of Solids and Materials

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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