The thermomechanics of plasticity and fracture

목차 (Table of Contents)

• CONTENTS
• Preface = xi
• Historical perspective = xv
• Notation = xvii
• 1 Introduction to plasticity: experimental facts = 1
• 1.1 Elastic and plastic behaviours = 1
• 1.2 Influence of the strain rate = 7
• 1.3 Other effects = 9
• 1.4 The plastic-hardening threshold: experimental data = 11
• 1.5 Examples of plastic-flow criteria = 17
• 1.6 Conclusions: working hypotheses in elastoplasticity = 24
• Problems for Chapter 1 = 25
• 2 Thermomechanics of elastoviscoplastic continua = 30
• 2.1 The small-perturbation hypothesis = 30
• 2.2 General principles of continuous-media thermomechanics = 32
• 2.2.1 Principle of virtual power (PVP) = 32
• 2.2.2 Principles (laws) of thermodynamics for continuous media = 36
• 2.3 Using the Clausius-Duhem inequality = 38
• 2.4 Particular cases of solid media = 40
• 2.4.1 Neither plastic strain nor associated phenomena = 40
• 2.4.2 Maxwell's viscoelasticity = 41
• 2.4.3 Thermoelasticity = 43
• 2.4.4 The difference between viscous and plastic phenomena = 43
• Problems for Chapter 2 = 46
• 3 Small-strain elastoplasticity = 50
• 3.1 Reminder of the thermomechanical formulation = 50
• 3.1.1 The notion of normal dissipative mechanism = 50
• 3.1.2 Dissipation pseudo-potential = 52
• 3.1.3 Positively homogeneous dissipation functions of degree 1 = 53
• 3.2 Perfect plasticity equations in SPH = 54
• 3.3 Incremental nature of the elastoplasticity laws = 57
• 3.4 Remarks = 61
• 3.4.1 Energy aspect = 61
• 3.4.2 Thermodynamic restriction on the convex C = 62
• 3.4.3 Regularity = 62
• 3.4.4 The Prandtl-Reuss relations = 62
• 3.4,5 The L$$\acute e$$vy-Mises relations = 63
• 3.4.6 The Hencky-Nadai relations = 63
• 3.5 Viscoplasticity = 63
• Problems for Chapter 3 = 65
• 4 Problems in perfect elastoplasticity = 69
• 4.1 Reminder of the perfect elastoplasticity equations = 69
• 4.2 Problem in terms of velocities = 72
• 4.2.1 The intuitive viewpoint = 72
• 4.2.2 The Greenberg minimum principle = 72
• 4.2.3 The Hodge-Prager minimum principle = 73
• 4.2.4 Mathematical analysis of quasi-static evolution = 77
• 4.2.5 Evolution in stresses = 77
• 4.2.6 Evolution of plastic strains = 80
• 4.3 Asymptotic behaviour: shakedown = 81
• 4.3.1 Practical motivation = 81
• 4.3.2 The Melan-Koiter Theorem = 82
• 4.4 Remark on discontinuities = 85
• Appendix to Chapter 4: minimum principles in elasticity = 85
• Problems for Chapter 4 = 89
• 5 Elastoplasticity with strain-hardening = 94
• 5.1 Generalized standard media = 94
• 5.1.1 The basic idea = 94
• 5.1.2 Generalization = 96
• 5.1.3 Examples = 97
• 5.2 Relations between velocities; incremental constitutive equations = 107
• 5.3 Stability in Ilyushin's sense = 111
• 5.4 Elastoplastic evolution in the presence of hardening = 113
• 5.5 Simplified abstract formulation = 114
• Problems for Chapter 5 = 116
• 6 Elements of limit analysis = 121
• 6.1 The notion of limit load = 12l
• 6.1.1 Characterization of the limit load = 122
• 6.1.2 Case of the rigid-plastic model = 123
• 6.1.3 Example: spherical envelope under pressure = 123
• 6.2 Computation of the limit load = 127
• 6.2.1 Generalities = 127
• 6.2.2 Static method = 129
• 6.2.3 Kinematic method = 130
• 6.3 Example of a foundation's limit load = 130
• Problems for Chapter 6 = 132
• 7 Crack propagation and fracture mechanics = 136
• 7.1 Introduction and elementary notions = 136
• 7.2 The notion of singularity = 139
• 7.3 The energy aspect of brittle fracture = 144
• 7.4 The Rice-Eshelby-Cherepanov integral = 148
• 7.5 Global potential, generalized Rice integral, energy-release rate = 149
• 7.6 Quasi-static evolution of a crack system in an elastic solid in brittle fracture = 150
• 7.7 Similarity between plasticity and fracture = 153
• 7.8 The Barenblatt theory = 155
• 7.9 Introduction of a plastic zone = 156
• Problems for Chapter 7 = 158
• 8 Elastoplasticity with finite strains = 162
• 8.1 Decomposition of elastoplastic strains = 162
• 8.2 Green-Naghdi decomposition = 166
• 8.3 Lee decomposition = 167
• 8.4 Evolution equation (normality rule) = 169
• Problems for Chapter 8 = 171
• 9 Homogenization of elastoplastic composites = 174
• 9.1 Notion of homogenization = 174
• 9.2 Notion of representative volume element and localization = 175
• 9.2.1 Representative volume element (RVE) = 175
• 9.2.2 Localization process = 176
• 9.2.3 The Hill-Mandel principle of macro-homogeneity = 177
• 9.2.4 Functional notation = 178
• 9.3 The example of pure elasticity = 179
• 9.3.1 The localization problem = 179
• 9.3.2 Case where ε is prescribed = 180
• 9.3.3 Case where Σ is prescribed = 181
• 9.3.4 Equivalence between 'prescribed stress' and 'prescribed strain' = 182
• 9.4 Elastoplastic constituents = 183
• 9.4.1 Macroscopic potentials = 183
• 9.4.2 Stability in the sense of Drucker = 185
• 9.4.3 Macroscopic loading surface, macroscopic 'convex' = 186
• 9.5 Structure of macroscopic constitutive equations = 187
• 9.5.1 State variables = 187
• 9.5.2 Internal energy of the macroscopic material = 188
• 9.5.3 Equations of state = 188
• 9.5.4 Example of an approximate model = 189
• 9.6 First example: composite with unidirectional fibres = 191
• 9.7 Second example: polycrystals = 194
• 9.7.1 The monocrystal = 194
• 9.7.2 The polycrystal = 195
• 9.8 Notion of limit analysis for composites = 197
• 9.8.1 Extremal flow surface = 197
• 9.8.2 Determination of homogenized plastically admissible stresses = 198
• 9.9 Homogenization of cracked materials = 199
• Problems for Chapter 9 = 202
• 10 Coupling between plasticity and damage = 206
• 10.1 Notion of damage = 206
• 10.2 Thermodynamic formulation in SPH = 207
• 10.3 Elastoplasticity of a damaged body = 208
• 10.3.1 Damage criterion = 208
• 10.3.2 Evolution of damage parameters = 210
• 10.3.3 Plastic microstrains = 211
• 10.3.4 Coupling with plasticity = 212
• 10.4 Example of a complete model with ductile damage = 213
• Problems for Chapter 10 = 214
• 11 Numerical solution of plasticity problems = 219
• 11.1 Introduction = 219
• 11.2 Elementary notions on numerical computations = 220
• 11.3 Application to elastoplasticity = 220
• 11.3.1 Explicit scheme = 220
• 11.3.2 Implicit scheme = 221
• 11.3.3 Incremental problem for the implicit scheme = 223
• 11.3.4 Example of iterative method (Ilyushin) = 223
• 11.3.5 An elastoplastic thin flat plate with a thermal loading = 226
• 11.4 Application of the finite-element method = 228
• 11.5 Examples of computations by FEM in elastoplasticity = 230
• 11.5.1 Elastoplastic torsion of a cylindrical rod with a multiconnected section = 230
• 11.5.2 Traction of a cracked rectangular plate = 233
• Problems for Chapter 11 = 235
• 12 Experimental study using infrared thermography = 245
• 12.1 Heat equation in a deformable solid = 245
• 12.2 Linearization about a natural reference state = 248
• 12.3 Method of infrared thermography = 250
• 12.4 Temperature distribution in fracture = 252
• 12.4.1 Consequences of thermodynamic laws = 252
• 12.4.2 Singularity of the temperature distribution = 256
• 12.5 Illustrative examples = 258
• Problems for Chapter 12 = 258
• Appendix 1 Thermodynamics of continuous media = 262
• A1.1 General notions = 262
• A1.1.1 Thermodynamic systems = 262
• Al.1.2 Thermodynamic state variables = 263
• A1.1.3 Thermodynamic state = 263
• A1.2 Thermostatics = 264
• A1.2.1 Axioms of thermostatics = 264
• A1.2.2 Scaling of temperature, Carnot's Theorem = 267
• A1.2.3 Thermodynamic potentials = 268
• A1.2.4 The evolution of real systems = 270
• A1.3 Thermodynamics = 272
• A1.3.1 The theory of irreversible processes = 272
• A1.3.2 The'rational' theory of Coleman and Noll = 276
• A1.3.3 Theory with internal variables = 276
• A1.3.3.1 General properties = 276
• A1.3.3.2 Local accompanying state = 278
• A1.3.3.3 Evolution laws for internal variables = 280
• Appendix 2 Convexity = 283
• A2.1 Definitions = 283
• A2.1.1 Convex function = 283
• A2.1.2 Indicator function of a convex set = 283
• A2.2 Subdifferentials = 285
• A2.3 Lower semicontinuity = 288
• A2.4 Conjugate functions, Legendre-Fenchel transformation = 288
• A2.5 Minimization of functions = 291
• Appendix 3 Analytic solutions of some problems in elastoplasticity = 293
• A3.1 Elastoplastic loading of a wedge = 293
• A3.1.1 General equations = 293
• A3.1.2 Elastic law of state = 294
• A3.1.3 Prandtl-Reuss equations = 295
• A3.1.4 The full elastic solution = 295
• A3.1.5 Elastoplastic border = 296
• A3.1.6 The elastoplastic solution = 297
• A3.2 Elastoplastic torsion of a circular shaft = 299
• A3.2.1 Elastic solution = 299
• A3.2.2 Elastoplastic solution = 300
• A3.3 Tube subjected to combined torsion and simple traction = 302
• A3.4 Cyclic torsion of a composite with unidirectional fibres = 304
• A3.4.1 Basic equations = 305
• A3.4.2 Torsion of a slice = 306
• A3.4.3 Material obeying a generalized Tresca criterion = 308
• A3.5 Problems with hardening = 309
• Appendix 4 Analytic computation of stress-intensity factors = 313
• A4.1 Plane problems in isotropic linear elasticity = 313
• A4.2 Stress-intensity factor at the crack tip = 316
• A4.3 Remark on numerical computations of stress-intensity factors = 321
• Further reading = 324
• Bibliography = 326
• Index = 341