Mechanics of solids and materials:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2006
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Table of contents Publisher description Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XX, 860 S. |
| ISBN: | 0521859794 9780521859790 |
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MARC
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| 100 | 1 | |a Asaro, Robert J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mechanics of solids and materials |c Robert J. Asaro ; Vlado A. Lubarda |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2006 | |
| 300 | |a XX, 860 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Matériaux - Propriétés mécaniques | |
| 650 | 4 | |a Mécanique appliquée | |
| 650 | 4 | |a Mechanics, Applied | |
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| 700 | 1 | |a Lubarda, Vlado A. |e Verfasser |4 aut | |
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| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0633/2005025722-d.html |3 Publisher description | |
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| adam_text | Contents
Preface page xix
PART 1: MATHEMATICAL PRELIMINARIES
1 Vectors and Tensors 1
1.1. Vector Algebra 1
1.2. Coordinate Transformation: Rotation
of Axes 4
1.3. Second-Rank Tensors 5
1.4. Symmetric and Antisymmetric Tensors 5
1.5. Prelude to Invariants of Tensors 6
1.6. Inverse of a Tensor 7
1.7. Additional Proofs 7
1.8. Additional Lemmas for Vectors 8
1.9. Coordinate Transformation of Tensors 9
1.10. Some Identities with Indices 10
1.11. Tensor Product 10
1.12. Orthonormal Basis 11
1.13. Eigenvectors and Eigenvalues 12
1.14. Symmetric Tensors 14
1.15. Positive Definiteness of a Tensor 14
1.16. Antisymmetric Tensors 15
1.16.1. Eigenvectors of W 15
1.17. Orthogonal Tensors 17
1.18. Polar Decomposition Theorem 19
1.19. Polar Decomposition: Physical Approach 20
1.19.1. Left and Right Stretch Tensors 21
1.19.2. Principal Stretches 21
1.20. The Cayley-Hamilton Theorem 22
1.21. Additional Lemmas for Tensors 23
1.22. Identities and Relations Involving
V Operator 23
1.23. Suggested Reading 25
v
vi Contents
2 Basic Integral Theorems 26
2.1. Gauss and Stokes s Theorems 26
2.1.1. Applications of Divergence Theorem 27
2.2. Vector and Tensor Fields: Physical Approach 27
2.3. Surface Integrals: Gauss Law 28
2.4. Evaluating Surface Integrals 29
2.4.1. Application of the Concept of Flux 31
2.5. The Divergence 31
2.6. Divergence Theorem: Relation of Surface to Volume
Integrals 33
2.7. More on Divergence Theorem 34
2.8. Suggested Reading 35
3 Fourier Series and Fourier Integrals 36
3.1. Fourier Series 36
3.2. Double Fourier Series 37
3.2.1. Double Trigonometric Series 38
3.3. Integral Transforms 39
3.4. Dirichlet s Conditions 42
3.5. Integral Theorems 46
3.6. Convolution Integrals 48
3.6.1. Evaluation of Integrals by Use of Convolution
Theorems 49
3.7. Fourier Transforms of Derivatives of f(x) 49
3.8. Fourier Integrals as Limiting Cases of Fourier Series 50
3.9. Dirac Delta Function 51
3.10. Suggested Reading 52
PART 2: CONTINUUM MECHANICS
4 Kinematics of Continuum 55
4.1. Preliminaries 55
4.2. Uniaxial Strain 56
4.3. Deformation Gradient 57
4.4. Strain Tensor 58
4.5. Stretch and Normal Strains 60
4.6. Angle Change and Shear Strains 60
4.7. Infinitesimal Strains 61
4.8. Principal Stretches 62
4.9. Eigenvectors and Eigenvalues of Deformation Tensors 63
4.10. Volume Changes 63
4.11. Area Changes 64
4.12. Area Changes: Alternative Approach 65
4.13. Simple Shear of a Thick Plate with a Central Hole 66
4.14. Finite vs. Small Deformations 68
4.15. Reference vs. Current Configuration 69
4.16. Material Derivatives and Velocity 71
4.17. Velocity Gradient 71
Contents vii
4.18. Deformation Rate and Spin 74
4.19. Rate of Stretching and Shearing 75
4.20. Material Derivatives of Strain Tensors: E vs. D 76
4.21. Rate of F in Terms of Principal Stretches 78
4.21.1. Spins of Lagrangian and Eulerian Triads 81
4.22. Additional Connections Between Current and Reference
State Representations 82
4.23. Transport Formulae 83
4.24. Material Derivatives of Volume, Area, and Surface Integrals:
Transport Formulae Revisited 84
4.25. Analysis of Simple Shearing 85
4.26. Examples of Particle and Plane Motion 87
4.27. Rigid Body Motions 88
4.28. Behavior under Superposed Rotation 89
4.29. Suggested Reading 90
5 Kinetics of Continuum 92
5.1. Traction Vector and Stress Tensor 92
5.2. Equations of Equilibrium 94
5.3. Balance of Angular Momentum: Symmetry of a 95
5.4. Principal Values of Cauchy Stress 96
5.5. Maximum Shear Stresses 97
5.6. Nominal Stress 98
5.7. Equilibrium in the Reference State 99
5.8. Work Conjugate Connections 100
5.9. Stress Deviator 102
5.10. Frame Indifference 102
5.11. Continuity Equation and Equations of Motion 107
5.12. Stress Power 108
5.13. The Principle of Virtual Work 109
5.14. Generalized Clapeyron s Formula 111
5.15. Suggested Reading 111
6 Thermodynamics of Continuum 113
6.1. First Law of Thermodynamics: Energy Equation 113
6.2. Second Law of Thermodynamics: Clausius-Duhem
Inequality 114
6.3. Reversible Thermodynamics 116
6.3.1. Thermodynamic Potentials 116
6.3.2. Specific and Latent Heats 118
6.3.3. Coupled Heat Equation 119
6.4. Thermodynamic Relationships with p, V, T, and s 120
6.4.1. Specific and Latent Heats 121
6.4.2. Coefficients of Thermal Expansion and
Compressibility 122
6.5. Theoretical Calculations of Heat Capacity 123
6.6. Third Law of Thermodynamics 125
6.7. Irreversible Thermodynamics 127
6.7.1. Evolution of Internal Variables 129
viii Contents
6.8. Gibbs Conditions of Thermodynamic Equilibrium 129
6.9. Linear Thermoelastidty 130
6.10. Thermodynamic Potentials in Linear Thermoelasticity 132
6.10.1. Internal Energy 132
6.10.2. Helmholtz Free Energy 133
6.10.3. Gibbs Energy 134
6.10.4. Enthalpy Function 135
6.11. Uniaxial Loading and Thermoelastic Effect 136
6.12. Thermodynamics of Open Systems: Chemical
Potentials 139
6.13. Gibbs-Duhem Equation 141
6.14. Chemical Potentials for Binary Systems 142
6.15. Configurational Entropy 143
6.16. Ideal Solutions 144
6.17. Regular Solutions for Binary Alloys 145
6.18. Suggested Reading 147
7 Nonlinear Elasticity 148
7.1. Green Elasticity 148
7.2. Isotropic Green Elasticity 150
7.3. Constitutive Equations in Terms of B 151
7.4. Constitutive Equations in Terms of Principal Stretches 152
7.5. Incompressible Isotropic Elastic Materials 153
7.6. Elastic Moduli Tensors 153
7.7. Instantaneous Elastic Moduli 155
7.8. Elastic Pseudomoduli 155
7.9. Elastic Moduli of Isotropic Elasticity 156
7.10. Elastic Moduli in Terms of Principal Stretches 157
7.11. Suggested Reading 158
PART 3: LINEAR ELASTICITY
8 Governing Equations of Linear Elasticity 161
8.1. Elementary Theory of Isotropic Linear Elasticity 161
8.2. Elastic Energy in Linear Elasticity 163
8.3. Restrictions on the Elastic Constants 164
8.3.1. Material Symmetry 164
8.3.2. Restrictions on the Elastic Constants 168
8.4. Compatibility Relations 169
8.5. Compatibility Conditions: Cesaro Integrals 170
8.6. Beltrami-Michell Compatibility Equations 172
8.7. Navier Equations of Motion 172
8.8. Uniqueness of Solution to Linear Elastic Boundary Value
Problem 174
8.8.1. Statement of the Boundary Value Problem 174
8.8.2. Uniqueness of the Solution 174
8.9. Potential Energy and Variational Principle 175
8.9.1. Uniqueness of the Strain Field 177
Contents ix
8.10. Betti s Theorem of Linear Elasticity 177
8.11. Plane Strain 178
8.11.1. Plane Stress 179
8.12. Governing Equations of Plane Elasticity 180
8.13. Thermal Distortion of a Simple Beam 180
8.14. Suggested Reading 182
9 Elastic Beam Problems 184
9.1. A Simple 2D Beam Problem 184
9.2. Polynomial Solutions to V4 / = 0 185
9.3. A Simple Beam Problem Continued 186
9.3.1. Strains and Displacements for 2D Beams 187
9.4. Beam Problems with Body Force Potentials 188
9.5. Beam under Fourier Loading 190
9.6. Complete Boundary Value Problems for Beams 193
9.6.1. Displacement Calculations 196
9.7. Suggested Reading 198
10 Solutions in Polar Coordinates 199
10.1. Polar Components of Stress and Strain 199
10.2. Plate with Circular Hole 201
10.2.1. Far Field Shear 201
10.2.2. Far Field Tension 203
10.3. Degenerate Cases of Solution in Polar Coordinates 204
10.4. Curved Beams: Plane Stress 206
10.4.1. Pressurized Cylinder 209
10.4.2. Bending of a Curved Beam 210
10.5. Axisymmetric Deformations 211
10.6. Suggested Reading 213
11 Torsion and Bending of Prismatic Rods 214
11.1. Torsion of Prismatic Rods 214
11.2. Elastic Energy of Torsion 216
11.3. Torsion of a Rod with Rectangular Cross Section 217
11.4. Torsion of a Rod with Elliptical Cross Section 221
11.5. Torsion of a Rod with Multiply Connected Cross Sections 222
11.5.1. Hollow Elliptical Cross Section 224
11.6. Bending of a Cantilever 225
11.7. Elliptical Cross Section 227
11.8. Suggested Reading 228
12 Semi-Infinite Media 229
12.1. Fourier Transform of Biharmonic Equation 229
12.2. Loading on a Half-Plane 230
12.3. Half-Plane Loading: Special Case 232
12.4. Symmetric Half-Plane Loading 234
12.5. Half-Plane Loading: Alternative Approach 235
12.6. Additional Half-Plane Solutions 237
x Contents
12.6.1. Displacement Fields in Half-Spaces 238
12.6.2. Boundary Value Problem 239
12.6.3. Specific Example 240
12.7. Infinite Strip 242
12.7.1. Uniform Loading: -a x a 243
12.7.2. Symmetrical Point Loads 244
12.8. Suggested Reading 245
13 Isotropic 3D Solutions 246
13.1. Displacement-Based Equations of Equilibrium 246
13.2. Boussinesq-Papkovitch Solutions 247
13.3. Spherically Symmetrical Geometries 248
13.3.1. Internally Pressurized Sphere 249
13.4. Pressurized Sphere: Stress-Based Solution 251
13.4.1. Pressurized Rigid Inclusion 252
13.4.2. Disk with Circumferential Shear 253
13.4.3. Sphere Subject to Temperature Gradients 254
13.5. Spherical Indentation 254
13.5.1. Displacement-Based Equilibrium 255
13.5.2. Strain Potentials 256
13.5.3. Point Force on a Half-Plane 257
13.5.4. Hemispherical Load Distribution 258
13.5.5. Indentation by a Spherical Ball 259
13.6. Point Forces on Elastic Half-Space 261
13.7. Suggested Reading 263
14 Anisotropic 3D Solutions 264
14.1. Point Force 264
14.2. Green s Function 264
14.3. Isotropic Green s Function 268
14.4. Suggested Reading 270
15 Plane Contact Problems 271
15.1. Wedge Problem 271
15.2. Distributed Contact Forces 274
15.2.1. Uniform Contact Pressure 275
15.2.2. Uniform Tangential Force 277
15.3. Displacement-Based Contact: Rigid Flat Punch 277
15.4. Suggested Reading 279
16 Deformation of Plates 280
16.1. Stresses and Strains of Bent Plates 280
16.2. Energy of Bent Plates 281
16.3. Equilibrium Equations for a Plate 282
16.4. Shear Forces and Bending and Twisting Moments 285
16.5. Examples of Plate Deformation 287
16.5.1. Clamped Circular Plate 287
16.5.2. Circular Plate with Simply Supported Edges 288
Contents xi
16.5.3. Circular Plate with Concentrated Force 288
16.5.4. Peeled Surface Layer 288
16.6. Rectangular Plates 289
16.6.1. Uniformly Loaded Rectangular Plate 290
16.7. Suggested Reading 291
PART 4: MICROMECHANICS
17 Dislocations and Cracks: Elementary Treatment 293
17.1. Dislocations 293
17.1.1. Derivation of the Displacement Field 294
17.2. Tensile Cracks 295
17.3. Suggested Reading 298
18 Dislocations in Anisotropic Media 299
18.1. Dislocation Character and Geometry 299
18.2. Dislocations in Isotropic Media 302
18.2.1. Infinitely Long Screw Dislocations 302
18.2.2. Infinitely Long Edge Dislocations 303
18.2.3. Infinitely Long Mixed Segments 303
18.3. Planar Geometric Theorem 305
18.4. Applications of the Planar Geometric Theorem 308
18.4.1. Angular Dislocations 311
18.5. A 3D Geometrical Theorem 312
18.6. Suggested Reading 314
19 Cracks in Anisotropic Media 315
19.1. Dislocation Mechanics: Reviewed 315
19.2. Freely Slipping Crack 316
19.3. Crack Extension Force 319
19.4. Crack Faces Loaded by Tractions 320
19.5. Stress Intensity Factors and Crack Extension Force 322
19.5.1. Computation of the Crack Extension Force 323
19.6. Crack Tip Opening Displacement 325
19.7. Dislocation Energy Factor Matrix 325
19.8. Inversion of a Singular Integral Equation 328
19.9. 2D Anisotropic Elasticity - Stroh Formalism 329
19.9.1. Barnett-Lothe Tensors 332
19.10. Suggested Reading 334
20 The Inclusion Problem . 335
20.1. The Problem 335
20.2. Eshelby s Solution Setup 336
20.3. Calculation of the Constrained Fields: uc, ec, and ac 338
20.4. Components of the Eshelby Tensor for Ellipsoidal Inclusion 341
20.5. Elastic Energy of an Inclusion 343
20.6. Inhomogeneous Inclusion: Uniform Transformation Strain 343
20.7. Nonuniform Transformation Strain Inclusion Problem 345
20.7.1. The Cases M= 0,1 349
xij Contents
20.8. Inclusions in Isotropic Media 350
20.8.1. Constrained Elastic Field 350
20.8.2. Field in the Matrix 351
20.8.3. Field at the Interface 352
20.8.4. Isotropic Spherical Inclusion 353
20.9. Suggested Reading 354
21 Forces and Energy in Elastic Systems 355
21.1. Free Energy and Mechanical Potential Energy 355
21.2. Forces of Translation 357
21.2.1. Force on an Interface 359
21.2.2. Finite Deformation Energy Momentum Tensor 360
21.3. Interaction Between Defects and Loading Mechanisms 362
21.3.1. Interaction Between Dislocations and
Inclusions 364
21.3.2. Force on a Dislocation Segment 365
21.4. Elastic Energy of a Dislocation 366
21.5. In-Plane Stresses of Straight Dislocation Lines 367
21.6. Chemical Potential 369
21.6.1. Force on a Defect due to a Free Surface 371
21.7. Applications of the / Integral 372
21.7.1. Force on a Clamped Crack 372
21.7.2. Application of the Interface Force to
Precipitation 372
21.8. Suggested Reading 374
22 Micropolar Elasticity 375
22.1. Introduction 375
22.2. Basic Equations of Couple-Stress Elasticity 376
22.3. Displacement Equations of Equilibrium 377
22.4. Correspondence Theorem of Couple-Stress Elasticity 378
22.5. Plane Strain Problems of Couple-Stress Elasticity 379
22.5.1. Mindlin s Stress Functions 380
22.6. Edge Dislocation in Couple-Stress Elasticity 381
22.6.1. Strain Energy 382
22.7. Edge Dislocation in a Hollow Cylinder 384
22.8. Governing Equations for Antiplane Strain 386
22.8.1. Expressions in Polar Coordinates 388
22.8.2. Correspondence Theorem for Antiplane Strain 389
22.9. Antiplane Shear of Circular Annulus 390
22.10. Screw Dislocation in Couple-Stress Elasticity 391
22.10.1. Strain Energy 392
22.11. Configurational Forces in Couple-Stress Elasticity 392
22.11.1. Reciprocal Properties 393
22.11.2. Energy due to Internal Sources of Stress 394
22.11.3. Energy due to Internal and External Sources of
Stress 394
22.11.4. The Force on an Elastic Singularity 395
Contents xiii
22.12. Energy-Momentum Tensor of a Couple-Stress Field 396
22.13. Basic Equations of Micropolar Elasticity 398
22.14. Noether s Theorem of Micropolar Elasticity 400
22.15. Conservation Integrals in Micropolar Elasticity 403
22.16. Conservation Laws for Plane Strain Micropolar Elasticity 404
22.17. M Integral of Micropolar Elasticity 404
22.18. Suggested Reading 406
PART 5: THIN FILMS AND INTERFACES
23 Dislocations in Bimaterials 407
23.1. Introduction 407
23.2. Screw Dislocation Near a Bimaterial Interface 407
23.2.1. Interface Screw Dislocation 409
23.2.2. Screw Dislocation in a Homogeneous Medium 409
23.2.3. Screw Dislocation Near a Free Surface 409
23.2.4. Screw Dislocation Near a Rigid Boundary 410
23.3. Edge Dislocation (bx) Near a Bimaterial Interface 410
23.3.1. Interface Edge Dislocation 415
23.3.2. Edge Dislocation in an Infinite Medium 417
23.3.3. Edge Dislocation Near a Free Surface 417
233 A. Edge Dislocation Near a Rigid Boundary 418
23.4. Edge Dislocation (by) Near a Bimaterial Interface 419
23.4.1. Interface Edge Dislocation 420
23.4.2. Edge Dislocation in an Infinite Medium 422
23.4.3. Edge Dislocation Near a Free Surface 422
23.4.4. Edge Dislocation Near a Rigid Boundary 423
23.5. Strain Energy of a Dislocation Near a Bimaterial Interface 423
23.5.1. Strain Energy of a Dislocation Near a
Free Surface 426
23.6. Suggested Reading 427
24 Strain Relaxation in Thin Films 428
24.1. Dislocation Array Beneath the Free Surface 428
24.2. Energy of a Dislocation Array 430
24.3. Strained-Layer Epitaxy 431
24.4. Conditions for Dislocation Array Formation 432
24.5. Frank and van der Merwe Energy Criterion 434
24.6. Gradual Strain Relaxation 436
24.7. Stability of Array Configurations 439
24.8. Stronger Stability Criteria 439
24.9. Further Stability Bounds 441
24.9.1. Lower Bound 441
24.9.2. Upper Bound 443
24.10. Suggested Reading 446
25 Stability of Planar Interfaces 447
25.1. Stressed Surface Problem 447
25.2. Chemical Potential 449
xiv Contents
25.3. Surface Diffusion and Interface Stability 450
25.4. Volume Diffusion and Interface Stability 451
25.5. 2D Surface Profiles and Surface Stability 455
25.6. Asymptotic Stresses for ID Surface Profiles 457
25.7. Suggested Reading 459
PART 6: PLASTICITY AND VISCOPLASTICITY
26 Phenomenological Plasticity 461
26.1. Yield Criteria for Multiaxial Stress States 462
26.2. Von Mises Yield Criterion 463
26.3. Tresca Yield Criterion 465
26.4. Mohr-Coulomb Yield Criterion 467
26.4.1. Drucker-Prager Yield Criterion 468
26.5. Gurson Yield Criterion for Porous Metals 470
26.6. Anisotropic Yield Criteria 470
26.7. Elastic-Plastic Constitutive Equations 471
26.8. Isotropic Hardening 473
26.8.1. h Flow Theory of Plasticity 474
26.9. Kinematic Hardening 475
26.9.1. Linear and Nonlinear Kinematic Hardening 477
26.10. Constitutive Equations for Pressure-Dependent Plasticity 478
26.11. Nonassociative Plasticity 480
26.12. Plastic Potential for Geomaterials 480
26.13. Rate-Dependent Plasticity 482
26.14. Deformation Theory of Plasticity 484
26.14.1. Rate-Type Formulation of Deformation Theory 485
26.14.2. Application beyond Proportional Loading 486
26.15. J2 Corner Theory 487
26.16. Rate-Dependent Flow Theory 489
26.16.1. Multiplicative Decomposition F = P • W 489
26.17. Elastic and Plastic Constitutive Contributions 491
26.17.1. Rate-Dependent J2 Flow Theory 492
26.18. A Rate Tangent Integration 493
26.19. Plastic Void Growth 495
26.19.1. Ideally Plastic Material 497
26.19.2. Incompressible Linearly Hardening Material 498
26.20. Suggested Reading 501
27 Micromechanics of Crystallographic Slip 502
27.1. Early Observations 502
27.2. Dislocations 508
27.2.1. Some Basic Properties of Dislocations in Crystals 511
21.1H. Strain Hardening, Dislocation Interactions, and
Dislocation Multiplication 514
27.3. Other Strengthening Mechanisms 517
27.4. Measurements of Latent Hardening 519
27.5. Observations of Slip in Single Crystals and Polycrystals at
Modest Strains 523
Contents x
27.6. Deformation Mechanisms in Nanocrystalline Grains 525
27.6.1. Background: AKK Model 530
27.6.2. Perspective on Discreteness 535
27.6.3. Dislocation and Partial Dislocation Slip Systems 535
27.7. Suggested Reading 537
28 Crystal Plasticity 538
28.1. Basic Kinematics 538
28.2. Stress and Stress Rates 541
28.2.1. Resolved Shear Stress 542
28.2.2. Rate-Independent Strain Hardening 544
28.3. Convected Elasticity 545
28.4. Rate-Dependent Slip 547
28.4.1. A Rate Tangent Modulus 548
28.5. Crystalline Component Forms 550
28.5.1. Additional Crystalline Forms 553
28.5.2. Component Forms on Laboratory Axes 555
28.6. Suggested Reading 555
29 The Nature of Crystalline Deformation: Localized Plastic
Deformation 557
29.1. Perspectives on Nonuniform and Localized Plastic Flow 557
29.1.1. Coarse Slip Bands and Macroscopic Shear Bands in
Simple Crystals 558
29.1.2. Coarse Slip Bands and Macroscopic Shear Bands in
Ordered Crystals 559
29.2. Localized Deformation in Single Slip 560
29.2.1. Constitutive Law for the Single Slip Crystal 560
29.2.2. Plastic Shearing with Non-Schmid Effects 560
29.2.3. Conditions for Localization 563
29.2.4. Expansion to the Order of a 565
29.2.5. Perturbations about the Slip and Kink Plane
Orientations 567
29.2.6. Isotropic Elastic Moduli 570
29.2.7. Particular Cases for Localization 571
29.3. Localization in Multiple Slip 576
29.3.1. Double Slip Model 576
29.3.2. Constitutive Law for the Double Slip Crystal 576
29.4. Numerical Results for Crystalline Deformation 580
29.4.1. Additional Experimental Observations 580
29.4.2. Numerical Observations 582
29.5. Suggested Reading 584
30 Polycrystal Plasticity 586
30.1. Perspectives on Polycrystalline Modeling and Texture
Development 586
30.2. Polycrystal Model 588
30.3. Extended Taylor Model 590
xvi Contents
30.4. Model Calculational Procedure 592
30.4.1. Texture Determinations 593
30.4.2. Yield Surface Determination 594
30.5. Deformation Theories and Path-Dependent Response 596
30.5.1. Specific Model Forms 597
30.5.2. Alternative Approach to a Deformation Theory 598
30.5.3. Nonproportional Loading 598
30.6. Suggested Reading 600
31 Laminate Plasticity 601
31.1. Laminate Model 601
31.2. Additional Kinematical Perspective 604
31.3. Final Constitutive Forms 604
31.3.1. Rigid-Plastic Laminate in Single Slip 605
31.4. Suggested Reading 607
PART 7: BIOMECHANICS
32 Mechanics of a Growing Mass 609
32.1. Introduction 609
32.2. Continuity Equation 610
32.2.1. Material Form of Continuity Equation 610
32.2.2. Quantities per Unit Initial and Current Mass 612
32.3. Reynolds Transport Theorem 612
32.4. Momentum Principles 614
32.4.1. Rate-Type Equations of Motion 615
32.5. Energy Equation 615
32.5.1. Material Form of Energy Equation 616
32.6. Entropy Equation 617
32.6.1. Material Form of Entropy Equation 618
32.6.2. Combined Energy and Entropy Equations 619
32.7. General Constitutive Framework 619
32.7.1. Thermodynamic Potentials per Unit Initial Mass 620
32.7.2. Equivalence of the Constitutive Structures 621
32.8. Multiplicative Decomposition of Deformation Gradient 622
32.8.1. Strain and Strain-Rate Measures 623
32.9. Density Expressions 624
32.10. Elastic Stress Response 625
32.11. Partition of the Rate of Deformation 626
32.12. Elastic Moduli Tensor 627
32.12.1. Elastic Moduli Coefficients 629
32.13. Elastic Strain Energy Representation 629
32.14. Evolution Equation for Stretch Ratio 630
32.15. Suggested Reading 631
33 Constitutive Relations for Membranes 633
33.1. Biological Membranes 633
33.2. Membrane Kinematics 634
Contents xvii
33.3. Constitutive Laws for Membranes 637
33.4. Limited Area Compressibility 638
33.5. Simple Triangular Networks 639
33.6. Suggested Reading 640
PART 8: SOLVED PROBLEMS
34 Solved Problems for Chapters 1-33 641
Bibliography 833
Index 853
|
| adam_txt |
Contents
Preface page xix
PART 1: MATHEMATICAL PRELIMINARIES
1 Vectors and Tensors 1
1.1. Vector Algebra 1
1.2. Coordinate Transformation: Rotation
of Axes 4
1.3. Second-Rank Tensors 5
1.4. Symmetric and Antisymmetric Tensors 5
1.5. Prelude to Invariants of Tensors 6
1.6. Inverse of a Tensor 7
1.7. Additional Proofs 7
1.8. Additional Lemmas for Vectors 8
1.9. Coordinate Transformation of Tensors 9
1.10. Some Identities with Indices 10
1.11. Tensor Product 10
1.12. Orthonormal Basis 11
1.13. Eigenvectors and Eigenvalues 12
1.14. Symmetric Tensors 14
1.15. Positive Definiteness of a Tensor 14
1.16. Antisymmetric Tensors 15
1.16.1. Eigenvectors of W 15
1.17. Orthogonal Tensors 17
1.18. Polar Decomposition Theorem 19
1.19. Polar Decomposition: Physical Approach 20
1.19.1. Left and Right Stretch Tensors 21
1.19.2. Principal Stretches 21
1.20. The Cayley-Hamilton Theorem 22
1.21. Additional Lemmas for Tensors 23
1.22. Identities and Relations Involving
V Operator 23
1.23. Suggested Reading 25
v
vi Contents
2 Basic Integral Theorems 26
2.1. Gauss and Stokes's Theorems 26
2.1.1. Applications of Divergence Theorem 27
2.2. Vector and Tensor Fields: Physical Approach 27
2.3. Surface Integrals: Gauss Law 28
2.4. Evaluating Surface Integrals 29
2.4.1. Application of the Concept of Flux 31
2.5. The Divergence 31
2.6. Divergence Theorem: Relation of Surface to Volume
Integrals 33
2.7. More on Divergence Theorem 34
2.8. Suggested Reading 35
3 Fourier Series and Fourier Integrals 36
3.1. Fourier Series 36
3.2. Double Fourier Series 37
3.2.1. Double Trigonometric Series 38
3.3. Integral Transforms 39
3.4. Dirichlet's Conditions 42
3.5. Integral Theorems 46
3.6. Convolution Integrals 48
3.6.1. Evaluation of Integrals by Use of Convolution
Theorems 49
3.7. Fourier Transforms of Derivatives of f(x) 49
3.8. Fourier Integrals as Limiting Cases of Fourier Series 50
3.9. Dirac Delta Function 51
3.10. Suggested Reading 52
PART 2: CONTINUUM MECHANICS
4 Kinematics of Continuum 55
4.1. Preliminaries 55
4.2. Uniaxial Strain 56
4.3. Deformation Gradient 57
4.4. Strain Tensor 58
4.5. Stretch and Normal Strains 60
4.6. Angle Change and Shear Strains 60
4.7. Infinitesimal Strains 61
4.8. Principal Stretches 62
4.9. Eigenvectors and Eigenvalues of Deformation Tensors 63
4.10. Volume Changes 63
4.11. Area Changes 64
4.12. Area Changes: Alternative Approach 65
4.13. Simple Shear of a Thick Plate with a Central Hole 66
4.14. Finite vs. Small Deformations 68
4.15. Reference vs. Current Configuration 69
4.16. Material Derivatives and Velocity 71
4.17. Velocity Gradient 71
Contents vii
4.18. Deformation Rate and Spin 74
4.19. Rate of Stretching and Shearing 75
4.20. Material Derivatives of Strain Tensors: E vs. D 76
4.21. Rate of F in Terms of Principal Stretches 78
4.21.1. Spins of Lagrangian and Eulerian Triads 81
4.22. Additional Connections Between Current and Reference
State Representations 82
4.23. Transport Formulae 83
4.24. Material Derivatives of Volume, Area, and Surface Integrals:
Transport Formulae Revisited 84
4.25. Analysis of Simple Shearing 85
4.26. Examples of Particle and Plane Motion 87
4.27. Rigid Body Motions 88
4.28. Behavior under Superposed Rotation 89
4.29. Suggested Reading 90
5 Kinetics of Continuum 92
5.1. Traction Vector and Stress Tensor 92
5.2. Equations of Equilibrium 94
5.3. Balance of Angular Momentum: Symmetry of a 95
5.4. Principal Values of Cauchy Stress 96
5.5. Maximum Shear Stresses 97
5.6. Nominal Stress 98
5.7. Equilibrium in the Reference State 99
5.8. Work Conjugate Connections 100
5.9. Stress Deviator 102
5.10. Frame Indifference 102
5.11. Continuity Equation and Equations of Motion 107
5.12. Stress Power 108
5.13. The Principle of Virtual Work 109
5.14. Generalized Clapeyron's Formula 111
5.15. Suggested Reading 111
6 Thermodynamics of Continuum 113
6.1. First Law of Thermodynamics: Energy Equation 113
6.2. Second Law of Thermodynamics: Clausius-Duhem
Inequality 114
6.3. Reversible Thermodynamics 116
6.3.1. Thermodynamic Potentials 116
6.3.2. Specific and Latent Heats 118
6.3.3. Coupled Heat Equation 119
6.4. Thermodynamic Relationships with p, V, T, and s 120
6.4.1. Specific and Latent Heats 121
6.4.2. Coefficients of Thermal Expansion and
Compressibility 122
6.5. Theoretical Calculations of Heat Capacity 123
6.6. Third Law of Thermodynamics 125
6.7. Irreversible Thermodynamics 127
6.7.1. Evolution of Internal Variables 129
viii Contents
6.8. Gibbs Conditions of Thermodynamic Equilibrium 129
6.9. Linear Thermoelastidty 130
6.10. Thermodynamic Potentials in Linear Thermoelasticity 132
6.10.1. Internal Energy 132
6.10.2. Helmholtz Free Energy 133
6.10.3. Gibbs Energy 134
6.10.4. Enthalpy Function 135
6.11. Uniaxial Loading and Thermoelastic Effect 136
6.12. Thermodynamics of Open Systems: Chemical
Potentials 139
6.13. Gibbs-Duhem Equation 141
6.14. Chemical Potentials for Binary Systems 142
6.15. Configurational Entropy 143
6.16. Ideal Solutions 144
6.17. Regular Solutions for Binary Alloys 145
6.18. Suggested Reading 147
7 Nonlinear Elasticity 148
7.1. Green Elasticity 148
7.2. Isotropic Green Elasticity 150
7.3. Constitutive Equations in Terms of B 151
7.4. Constitutive Equations in Terms of Principal Stretches 152
7.5. Incompressible Isotropic Elastic Materials 153
7.6. Elastic Moduli Tensors 153
7.7. Instantaneous Elastic Moduli 155
7.8. Elastic Pseudomoduli 155
7.9. Elastic Moduli of Isotropic Elasticity 156
7.10. Elastic Moduli in Terms of Principal Stretches 157
7.11. Suggested Reading 158
PART 3: LINEAR ELASTICITY
8 Governing Equations of Linear Elasticity 161
8.1. Elementary Theory of Isotropic Linear Elasticity 161
8.2. Elastic Energy in Linear Elasticity 163
8.3. Restrictions on the Elastic Constants 164
8.3.1. Material Symmetry 164
8.3.2. Restrictions on the Elastic Constants 168
8.4. Compatibility Relations 169
8.5. Compatibility Conditions: Cesaro Integrals 170
8.6. Beltrami-Michell Compatibility Equations 172
8.7. Navier Equations of Motion 172
8.8. Uniqueness of Solution to Linear Elastic Boundary Value
Problem 174
8.8.1. Statement of the Boundary Value Problem 174
8.8.2. Uniqueness of the Solution 174
8.9. Potential Energy and Variational Principle 175
8.9.1. Uniqueness of the Strain Field 177
Contents ix
8.10. Betti's Theorem of Linear Elasticity 177
8.11. Plane Strain 178
8.11.1. Plane Stress 179
8.12. Governing Equations of Plane Elasticity 180
8.13. Thermal Distortion of a Simple Beam 180
8.14. Suggested Reading 182
9 Elastic Beam Problems 184
9.1. A Simple 2D Beam Problem 184
9.2. Polynomial Solutions to V4 / = 0 185
9.3. A Simple Beam Problem Continued 186
9.3.1. Strains and Displacements for 2D Beams 187
9.4. Beam Problems with Body Force Potentials 188
9.5. Beam under Fourier Loading 190
9.6. Complete Boundary Value Problems for Beams 193
9.6.1. Displacement Calculations 196
9.7. Suggested Reading 198
10 Solutions in Polar Coordinates 199
10.1. Polar Components of Stress and Strain 199
10.2. Plate with Circular Hole 201
10.2.1. Far Field Shear 201
10.2.2. Far Field Tension 203
10.3. Degenerate Cases of Solution in Polar Coordinates 204
10.4. Curved Beams: Plane Stress 206
10.4.1. Pressurized Cylinder 209
10.4.2. Bending of a Curved Beam 210
10.5. Axisymmetric Deformations 211
10.6. Suggested Reading 213
11 Torsion and Bending of Prismatic Rods 214
11.1. Torsion of Prismatic Rods 214
11.2. Elastic Energy of Torsion 216
11.3. Torsion of a Rod with Rectangular Cross Section 217
11.4. Torsion of a Rod with Elliptical Cross Section 221
11.5. Torsion of a Rod with Multiply Connected Cross Sections 222
11.5.1. Hollow Elliptical Cross Section 224
11.6. Bending of a Cantilever 225
11.7. Elliptical Cross Section 227
11.8. Suggested Reading 228
12 Semi-Infinite Media 229
12.1. Fourier Transform of Biharmonic Equation 229
12.2. Loading on a Half-Plane 230
12.3. Half-Plane Loading: Special Case 232
12.4. Symmetric Half-Plane Loading 234
12.5. Half-Plane Loading: Alternative Approach 235
12.6. Additional Half-Plane Solutions 237
x Contents
12.6.1. Displacement Fields in Half-Spaces 238
12.6.2. Boundary Value Problem 239
12.6.3. Specific Example 240
12.7. Infinite Strip 242
12.7.1. Uniform Loading: -a x a 243
12.7.2. Symmetrical Point Loads 244
12.8. Suggested Reading 245
13 Isotropic 3D Solutions 246
13.1. Displacement-Based Equations of Equilibrium 246
13.2. Boussinesq-Papkovitch Solutions 247
13.3. Spherically Symmetrical Geometries 248
13.3.1. Internally Pressurized Sphere 249
13.4. Pressurized Sphere: Stress-Based Solution 251
13.4.1. Pressurized Rigid Inclusion 252
13.4.2. Disk with Circumferential Shear 253
13.4.3. Sphere Subject to Temperature Gradients 254
13.5. Spherical Indentation 254
13.5.1. Displacement-Based Equilibrium 255
13.5.2. Strain Potentials 256
13.5.3. Point Force on a Half-Plane 257
13.5.4. Hemispherical Load Distribution 258
13.5.5. Indentation by a Spherical Ball 259
13.6. Point Forces on Elastic Half-Space 261
13.7. Suggested Reading 263
14 Anisotropic 3D Solutions 264
14.1. Point Force 264
14.2. Green's Function 264
14.3. Isotropic Green's Function 268
14.4. Suggested Reading 270
15 Plane Contact Problems 271
15.1. Wedge Problem 271
15.2. Distributed Contact Forces 274
15.2.1. Uniform Contact Pressure 275
15.2.2. Uniform Tangential Force 277
15.3. Displacement-Based Contact: Rigid Flat Punch 277
15.4. Suggested Reading 279
16 Deformation of Plates 280
16.1. Stresses and Strains of Bent Plates 280
16.2. Energy of Bent Plates 281
16.3. Equilibrium Equations for a Plate 282
16.4. Shear Forces and Bending and Twisting Moments 285
16.5. Examples of Plate Deformation 287
16.5.1. Clamped Circular Plate 287
16.5.2. Circular Plate with Simply Supported Edges 288
Contents xi
16.5.3. Circular Plate with Concentrated Force 288
16.5.4. Peeled Surface Layer 288
16.6. Rectangular Plates 289
16.6.1. Uniformly Loaded Rectangular Plate 290
16.7. Suggested Reading 291
PART 4: MICROMECHANICS
17 Dislocations and Cracks: Elementary Treatment 293
17.1. Dislocations 293
17.1.1. Derivation of the Displacement Field 294
17.2. Tensile Cracks 295
17.3. Suggested Reading 298
18 Dislocations in Anisotropic Media 299
18.1. Dislocation Character and Geometry 299
18.2. Dislocations in Isotropic Media 302
18.2.1. Infinitely Long Screw Dislocations 302
18.2.2. Infinitely Long Edge Dislocations 303
18.2.3. Infinitely Long Mixed Segments 303
18.3. Planar Geometric Theorem 305
18.4. Applications of the Planar Geometric Theorem 308
18.4.1. Angular Dislocations 311
18.5. A 3D Geometrical Theorem 312
18.6. Suggested Reading 314
19 Cracks in Anisotropic Media 315
19.1. Dislocation Mechanics: Reviewed 315
19.2. Freely Slipping Crack 316
19.3. Crack Extension Force 319
19.4. Crack Faces Loaded by Tractions 320
19.5. Stress Intensity Factors and Crack Extension Force 322
19.5.1. Computation of the Crack Extension Force 323
19.6. Crack Tip Opening Displacement 325
19.7. Dislocation Energy Factor Matrix 325
19.8. Inversion of a Singular Integral Equation 328
19.9. 2D Anisotropic Elasticity - Stroh Formalism 329
19.9.1. Barnett-Lothe Tensors 332
19.10. Suggested Reading 334
20 The Inclusion Problem . 335
20.1. The Problem 335
20.2. Eshelby's Solution Setup 336
20.3. Calculation of the Constrained Fields: uc, ec, and ac 338
20.4. Components of the Eshelby Tensor for Ellipsoidal Inclusion 341
20.5. Elastic Energy of an Inclusion 343
20.6. Inhomogeneous Inclusion: Uniform Transformation Strain 343
20.7. Nonuniform Transformation Strain Inclusion Problem 345
20.7.1. The Cases M= 0,1 349
xij Contents
20.8. Inclusions in Isotropic Media 350
20.8.1. Constrained Elastic Field 350
20.8.2. Field in the Matrix 351
20.8.3. Field at the Interface 352
20.8.4. Isotropic Spherical Inclusion 353
20.9. Suggested Reading 354
21 Forces and Energy in Elastic Systems 355
21.1. Free Energy and Mechanical Potential Energy 355
21.2. Forces of Translation 357
21.2.1. Force on an Interface 359
21.2.2. Finite Deformation Energy Momentum Tensor 360
21.3. Interaction Between Defects and Loading Mechanisms 362
21.3.1. Interaction Between Dislocations and
Inclusions 364
21.3.2. Force on a Dislocation Segment 365
21.4. Elastic Energy of a Dislocation 366
21.5. In-Plane Stresses of Straight Dislocation Lines 367
21.6. Chemical Potential 369
21.6.1. Force on a Defect due to a Free Surface 371
21.7. Applications of the / Integral 372
21.7.1. Force on a Clamped Crack 372
21.7.2. Application of the Interface Force to
Precipitation 372
21.8. Suggested Reading 374
22 Micropolar Elasticity 375
22.1. Introduction 375
22.2. Basic Equations of Couple-Stress Elasticity 376
22.3. Displacement Equations of Equilibrium 377
22.4. Correspondence Theorem of Couple-Stress Elasticity 378
22.5. Plane Strain Problems of Couple-Stress Elasticity 379
22.5.1. Mindlin's Stress Functions 380
22.6. Edge Dislocation in Couple-Stress Elasticity 381
22.6.1. Strain Energy 382
22.7. Edge Dislocation in a Hollow Cylinder 384
22.8. Governing Equations for Antiplane Strain 386
22.8.1. Expressions in Polar Coordinates 388
22.8.2. Correspondence Theorem for Antiplane Strain 389
22.9. Antiplane Shear of Circular Annulus 390
22.10. Screw Dislocation in Couple-Stress Elasticity 391
22.10.1. Strain Energy 392
22.11. Configurational Forces in Couple-Stress Elasticity 392
22.11.1. Reciprocal Properties 393
22.11.2. Energy due to Internal Sources of Stress 394
22.11.3. Energy due to Internal and External Sources of
Stress 394
22.11.4. The Force on an Elastic Singularity 395
Contents xiii
22.12. Energy-Momentum Tensor of a Couple-Stress Field 396
22.13. Basic Equations of Micropolar Elasticity 398
22.14. Noether's Theorem of Micropolar Elasticity 400
22.15. Conservation Integrals in Micropolar Elasticity 403
22.16. Conservation Laws for Plane Strain Micropolar Elasticity 404
22.17. M Integral of Micropolar Elasticity 404
22.18. Suggested Reading 406
PART 5: THIN FILMS AND INTERFACES
23 Dislocations in Bimaterials 407
23.1. Introduction 407
23.2. Screw Dislocation Near a Bimaterial Interface 407
23.2.1. Interface Screw Dislocation 409
23.2.2. Screw Dislocation in a Homogeneous Medium 409
23.2.3. Screw Dislocation Near a Free Surface 409
23.2.4. Screw Dislocation Near a Rigid Boundary 410
23.3. Edge Dislocation (bx) Near a Bimaterial Interface 410
23.3.1. Interface Edge Dislocation 415
23.3.2. Edge Dislocation in an Infinite Medium 417
23.3.3. Edge Dislocation Near a Free Surface 417
233 A. Edge Dislocation Near a Rigid Boundary 418
23.4. Edge Dislocation (by) Near a Bimaterial Interface 419
23.4.1. Interface Edge Dislocation 420
23.4.2. Edge Dislocation in an Infinite Medium 422
23.4.3. Edge Dislocation Near a Free Surface 422
23.4.4. Edge Dislocation Near a Rigid Boundary 423
23.5. Strain Energy of a Dislocation Near a Bimaterial Interface 423
23.5.1. Strain Energy of a Dislocation Near a
Free Surface 426
23.6. Suggested Reading 427
24 Strain Relaxation in Thin Films 428
24.1. Dislocation Array Beneath the Free Surface 428
24.2. Energy of a Dislocation Array 430
24.3. Strained-Layer Epitaxy 431
24.4. Conditions for Dislocation Array Formation 432
24.5. Frank and van der Merwe Energy Criterion 434
24.6. Gradual Strain Relaxation 436
24.7. Stability of Array Configurations 439
24.8. Stronger Stability Criteria 439
24.9. Further Stability Bounds 441
24.9.1. Lower Bound 441
24.9.2. Upper Bound 443
24.10. Suggested Reading 446
25 Stability of Planar Interfaces 447
25.1. Stressed Surface Problem 447
25.2. Chemical Potential 449
xiv Contents
25.3. Surface Diffusion and Interface Stability 450
25.4. Volume Diffusion and Interface Stability 451
25.5. 2D Surface Profiles and Surface Stability 455
25.6. Asymptotic Stresses for ID Surface Profiles 457
25.7. Suggested Reading 459
PART 6: PLASTICITY AND VISCOPLASTICITY
26 Phenomenological Plasticity 461
26.1. Yield Criteria for Multiaxial Stress States 462
26.2. Von Mises Yield Criterion 463
26.3. Tresca Yield Criterion 465
26.4. Mohr-Coulomb Yield Criterion 467
26.4.1. Drucker-Prager Yield Criterion 468
26.5. Gurson Yield Criterion for Porous Metals 470
26.6. Anisotropic Yield Criteria 470
26.7. Elastic-Plastic Constitutive Equations 471
26.8. Isotropic Hardening 473
26.8.1. h Flow Theory of Plasticity 474
26.9. Kinematic Hardening 475
26.9.1. Linear and Nonlinear Kinematic Hardening 477
26.10. Constitutive Equations for Pressure-Dependent Plasticity 478
26.11. Nonassociative Plasticity 480
26.12. Plastic Potential for Geomaterials 480
26.13. Rate-Dependent Plasticity 482
26.14. Deformation Theory of Plasticity 484
26.14.1. Rate-Type Formulation of Deformation Theory 485
26.14.2. Application beyond Proportional Loading 486
26.15. J2 Corner Theory 487
26.16. Rate-Dependent Flow Theory 489
26.16.1. Multiplicative Decomposition F = P • W 489
26.17. Elastic and Plastic Constitutive Contributions 491
26.17.1. Rate-Dependent J2 Flow Theory 492
26.18. A Rate Tangent Integration 493
26.19. Plastic Void Growth 495
26.19.1. Ideally Plastic Material 497
26.19.2. Incompressible Linearly Hardening Material 498
26.20. Suggested Reading 501
27 Micromechanics of Crystallographic Slip 502
27.1. Early Observations 502
27.2. Dislocations 508
27.2.1. Some Basic Properties of Dislocations in Crystals 511
21.1H. Strain Hardening, Dislocation Interactions, and
Dislocation Multiplication 514
27.3. Other Strengthening Mechanisms 517
27.4. Measurements of Latent Hardening 519
27.5. Observations of Slip in Single Crystals and Polycrystals at
Modest Strains 523
Contents x\
27.6. Deformation Mechanisms in Nanocrystalline Grains 525
27.6.1. Background: AKK Model 530
27.6.2. Perspective on Discreteness 535
27.6.3. Dislocation and Partial Dislocation Slip Systems 535
27.7. Suggested Reading 537
28 Crystal Plasticity 538
28.1. Basic Kinematics 538
28.2. Stress and Stress Rates 541
28.2.1. Resolved Shear Stress 542
28.2.2. Rate-Independent Strain Hardening 544
28.3. Convected Elasticity 545
28.4. Rate-Dependent Slip 547
28.4.1. A Rate Tangent Modulus 548
28.5. Crystalline Component Forms 550
28.5.1. Additional Crystalline Forms 553
28.5.2. Component Forms on Laboratory Axes 555
28.6. Suggested Reading 555
29 The Nature of Crystalline Deformation: Localized Plastic
Deformation 557
29.1. Perspectives on Nonuniform and Localized Plastic Flow 557
29.1.1. Coarse Slip Bands and Macroscopic Shear Bands in
Simple Crystals 558
29.1.2. Coarse Slip Bands and Macroscopic Shear Bands in
Ordered Crystals 559
29.2. Localized Deformation in Single Slip 560
29.2.1. Constitutive Law for the Single Slip Crystal 560
29.2.2. Plastic Shearing with Non-Schmid Effects 560
29.2.3. Conditions for Localization 563
29.2.4. Expansion to the Order of a 565
29.2.5. Perturbations about the Slip and Kink Plane
Orientations 567
29.2.6. Isotropic Elastic Moduli 570
29.2.7. Particular Cases for Localization 571
29.3. Localization in Multiple Slip 576
29.3.1. Double Slip Model 576
29.3.2. Constitutive Law for the Double Slip Crystal 576
29.4. Numerical Results for Crystalline Deformation 580
29.4.1. Additional Experimental Observations 580
29.4.2. Numerical Observations 582
29.5. Suggested Reading 584
30 Polycrystal Plasticity 586
30.1. Perspectives on Polycrystalline Modeling and Texture
Development 586
30.2. Polycrystal Model 588
30.3. Extended Taylor Model 590
xvi Contents
30.4. Model Calculational Procedure 592
30.4.1. Texture Determinations 593
30.4.2. Yield Surface Determination 594
30.5. Deformation Theories and Path-Dependent Response 596
30.5.1. Specific Model Forms 597
30.5.2. Alternative Approach to a Deformation Theory 598
30.5.3. Nonproportional Loading 598
30.6. Suggested Reading 600
31 Laminate Plasticity 601
31.1. Laminate Model 601
31.2. Additional Kinematical Perspective 604
31.3. Final Constitutive Forms 604
31.3.1. Rigid-Plastic Laminate in Single Slip 605
31.4. Suggested Reading 607
PART 7: BIOMECHANICS
32 Mechanics of a Growing Mass 609
32.1. Introduction 609
32.2. Continuity Equation 610
32.2.1. Material Form of Continuity Equation 610
32.2.2. Quantities per Unit Initial and Current Mass 612
32.3. Reynolds Transport Theorem 612
32.4. Momentum Principles 614
32.4.1. Rate-Type Equations of Motion 615
32.5. Energy Equation 615
32.5.1. Material Form of Energy Equation 616
32.6. Entropy Equation 617
32.6.1. Material Form of Entropy Equation 618
32.6.2. Combined Energy and Entropy Equations 619
32.7. General Constitutive Framework 619
32.7.1. Thermodynamic Potentials per Unit Initial Mass 620
32.7.2. Equivalence of the Constitutive Structures 621
32.8. Multiplicative Decomposition of Deformation Gradient 622
32.8.1. Strain and Strain-Rate Measures 623
32.9. Density Expressions 624
32.10. Elastic Stress Response 625
32.11. Partition of the Rate of Deformation 626
32.12. Elastic Moduli Tensor 627
32.12.1. Elastic Moduli Coefficients 629
32.13. Elastic Strain Energy Representation 629
32.14. Evolution Equation for Stretch Ratio 630
32.15. Suggested Reading 631
33 Constitutive Relations for Membranes 633
33.1. Biological Membranes 633
33.2. Membrane Kinematics 634
Contents xvii
33.3. Constitutive Laws for Membranes 637
33.4. Limited Area Compressibility 638
33.5. Simple Triangular Networks 639
33.6. Suggested Reading 640
PART 8: SOLVED PROBLEMS
34 Solved Problems for Chapters 1-33 641
Bibliography 833
Index 853 |
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| author | Asaro, Robert J. Lubarda, Vlado A. |
| author_facet | Asaro, Robert J. Lubarda, Vlado A. |
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| dewey-full | 620.1 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
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| discipline | Physik |
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| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV021555229 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T14:32:50Z |
| indexdate | 2024-07-09T20:38:31Z |
| institution | BVB |
| isbn | 0521859794 9780521859790 |
| language | English |
| lccn | 2005025722 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014771241 |
| oclc_num | 61478721 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | XX, 860 S. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Asaro, Robert J. Verfasser aut Mechanics of solids and materials Robert J. Asaro ; Vlado A. Lubarda 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2006 XX, 860 S. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Matériaux - Propriétés mécaniques Mécanique appliquée Mechanics, Applied Festkörpermechanik (DE-588)4129367-8 gnd rswk-swf Festkörpermechanik (DE-588)4129367-8 s DE-604 Lubarda, Vlado A. Verfasser aut http://www.loc.gov/catdir/toc/ecip0518/2005025722.html Table of contents http://www.loc.gov/catdir/enhancements/fy0633/2005025722-d.html Publisher description HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014771241&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Asaro, Robert J. Lubarda, Vlado A. Mechanics of solids and materials Matériaux - Propriétés mécaniques Mécanique appliquée Mechanics, Applied Festkörpermechanik (DE-588)4129367-8 gnd |
| subject_GND | (DE-588)4129367-8 |
| title | Mechanics of solids and materials |
| title_auth | Mechanics of solids and materials |
| title_exact_search | Mechanics of solids and materials |
| title_exact_search_txtP | Mechanics of solids and materials |
| title_full | Mechanics of solids and materials Robert J. Asaro ; Vlado A. Lubarda |
| title_fullStr | Mechanics of solids and materials Robert J. Asaro ; Vlado A. Lubarda |
| title_full_unstemmed | Mechanics of solids and materials Robert J. Asaro ; Vlado A. Lubarda |
| title_short | Mechanics of solids and materials |
| title_sort | mechanics of solids and materials |
| topic | Matériaux - Propriétés mécaniques Mécanique appliquée Mechanics, Applied Festkörpermechanik (DE-588)4129367-8 gnd |
| topic_facet | Matériaux - Propriétés mécaniques Mécanique appliquée Mechanics, Applied Festkörpermechanik |
| url | http://www.loc.gov/catdir/toc/ecip0518/2005025722.html http://www.loc.gov/catdir/enhancements/fy0633/2005025722-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014771241&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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