This volume presents recent developments in the theory of defects and the mechanics of material forces. Most of the contributions were presented at the International Symposium on Defect and Material Forces (ISDMM2007), held in Aussois, France, March 25-29, 2007. The mechanics of material forces, originated in the works of Eshelby, provide a rational framework for the description of driving forces on evolving inhomogeneities and structural changes in continua. The general eshelbian mechanics formulation comes up with a unifying treatment of different phenomena like fracture and damage evolution, phase transitions, plasticity and dislocation motion, etc. The articles concern both theoretical and computational aspects of the material mechanics of defects. Among the addressed topics are fracture and damage, electromagnetoelasticity, plasticity, distributed dislocations, thermodynamics, poroelasticity, generalized continua, structural optimization, conservation laws and symmetries, multiscale approaches, and numerical solution strategies.
Author(s): Christian Dascalu, Gérard A. Maugin, Claude Stolz, Editors
Edition: 1
Publisher: Springer
Year: 2008
Language: English
Pages: 302
Tags: Механика;Механика деформируемого твердого тела;Механика разрушения;
Cover......Page 1
Defect and Material Mechanics......Page 3
ISBN-13: 9781402069284......Page 4
Table of Contents......Page 6
Preface......Page 9
Introduction......Page 11
Interacting cracks......Page 13
Interaction of an edge dislocation with a circular hole......Page 14
References......Page 19
Introduction......Page 21
The Lagrangian electromagnetic potentials......Page 22
Inverse variation and configurational forces......Page 23
Gauge dependence and gauge invariance......Page 24
Final comments......Page 26
References......Page 27
Introduction......Page 29
The role of the driving force in crack direction......Page 30
The energy functional for kinks and straight extensions......Page 31
Kinked configurations: conformal mapping......Page 32
Complex formula for the energy released......Page 33
Arbitrary extensions as virtual paths......Page 34
The energy released functional andthe anti-symmetry principle......Page 35
A simple setting for the boundary value problem......Page 36
The construction of the conformal map......Page 38
References......Page 40
Introduction......Page 43
Balance equations......Page 44
The material archetype, its implantsand evolution......Page 45
Thermodynamic restrictions......Page 47
Configurational balance......Page 48
References......Page 51
Introduction......Page 53
Invariant integrals and their use in elastostatic inverse problems......Page 54
Identification of a spherical inclusion using one static uniaxial tension test......Page 55
Some special cases......Page 59
Conclusion......Page 60
References......Page 61
Introduction: general relations......Page 63
Long spheroids......Page 65
Needle-like extremely rigid inclusions......Page 66
Flat soft inclusions......Page 67
Needle-like rigid inclusions......Page 68
Inclusions of intermediate rigidity......Page 69
Extremely rigid inclusions......Page 70
Conclusions......Page 71
References......Page 74
Introduction......Page 75
Second order elastic and plastic pairsof deformations......Page 77
Relationships between the connections attached to the plastic and elastic distortions......Page 78
Time-derivatives of the elastic connection with respect to relaxed configuration......Page 79
The macro and micro balance equations......Page 80
Free energy imbalance......Page 82
Thermodynamic restrictions......Page 83
Screw dislocations......Page 85
Characteristics of the plastic distortion in the case of screw dislocation......Page 86
References......Page 88
Introduction......Page 91
Basic concepts and equations of couple-stress elasticity......Page 92
Plane problems of couple-stress elasticity......Page 94
Anti-plane strain......Page 95
Glide dislocation......Page 96
Mode II crack......Page 97
Mode III crack......Page 101
Acknowledgements......Page 104
References......Page 109
Introduction......Page 111
Additional assumptions and remarks......Page 112
Case of elastic brittle material......Page 113
Conclusion......Page 114
References......Page 115
Introduction......Page 117
Spatial and material motion problem in nonlinear elastostatics......Page 118
Spatial and material motion problem in nonlinear electro-elastostatics......Page 119
Material force method......Page 120
Relation to J-integral......Page 121
Numerical example......Page 122
References......Page 123
Introduction......Page 125
Boundary value problem and variational formulation......Page 126
Finite element approach......Page 127
Concept......Page 128
Inequality constraints......Page 130
Staggered Newton scheme......Page 132
Sequence k......Page 133
Numerical experiment......Page 134
Conclusions......Page 138
Acknowledgements......Page 139
References......Page 140
Introduction......Page 141
Preliminaries......Page 142
General setting for optimal design......Page 143
A special objective function......Page 144
Sensitivity of the physical residual......Page 146
Sensitivity of the material residual......Page 147
The discrete optimization problem......Page 148
The discrete sensitivity equations......Page 149
Full Newton method......Page 150
Staggered solution method......Page 151
Steepest descent method......Page 152
Mesh optimization......Page 153
Shape optimization......Page 154
Sensitivity of the energy release rate......Page 157
Conclusions......Page 158
References......Page 162
Introduction......Page 165
Formulation......Page 166
A New Variational Principle......Page 167
References......Page 168
Introduction......Page 171
Generalized Tonti's diagram......Page 172
Duality in fracture mechanics......Page 173
Duality in plasticity......Page 174
Symmetry loss, dissipation and inverse problems......Page 175
Solution to the earthquake inverse problem......Page 176
References......Page 179
Introduction......Page 181
Configurational force balance......Page 182
Phase field potential......Page 183
Microstructure evolution---self organisation......Page 184
Defective electrode......Page 185
Summary......Page 186
References......Page 188
Introduction......Page 189
Virtual work and discretisation......Page 190
Variable power singular element......Page 191
Discrete Dirichlet functional......Page 192
Linear elasticity......Page 193
Kinematics and kinetics......Page 194
Weak form and discretisation......Page 195
Cracked specimen......Page 196
References......Page 197
Introduction......Page 199
Material setting......Page 200
Jump relations at a front......Page 201
Phase-transition fronts in a bar......Page 202
Velocity of a phase boundary......Page 203
References......Page 205
Introduction......Page 207
Determination of eigenvalues and eigenvectorsin Williams-like asymptotic expansion......Page 209
Model of crack bridging......Page 210
Crack modeling by distributed dislocation technique......Page 211
Bridged crack modelling using weight function method......Page 214
Application of the -integral......Page 215
Determination of the generalized bridging stress intensity factor......Page 217
Numerical results......Page 218
Discussion......Page 220
Acknowledgements......Page 221
Introduction......Page 227
Description of the problem......Page 228
Derivation of Rivlin and Thomas (1953)......Page 229
Derivation of Eshelby (1975b)......Page 230
Application to the trousers test sample......Page 231
Remark on the definition of the configurational stress tensor......Page 232
Conclusion......Page 233
Introduction......Page 235
The eigentransformation, elastic transformation and deformation gradient......Page 236
Diffusion......Page 237
A time dependent isotropic surface......Page 240
Superficial dissipation inequality......Page 241
Concluding remarks......Page 242
Introduction......Page 243
Porosity-dependent elastic moduli......Page 247
The three regions (i), (ii) and (iii) in the plane (n,c)......Page 248
Local crack tip fields......Page 249
The eigenvalue problems......Page 250
The steps of the analysis......Page 251
Conditions on the process zone......Page 252
Flow conditions along the crack surfaces......Page 253
Crack propagation within the region (i)......Page 254
The Riemann--Hilbert problem......Page 255
Generic integrals......Page 256
Crack propagation within the region (ii)......Page 257
The Riemann--Hilbert problem......Page 258
Crack propagation within the region (iii)......Page 259
The Riemann--Hilbert problem......Page 260
The speeds c*=c*(n) separating the region (iii) in two domains......Page 261
Comparison crack without a process zoneand first order discontinuities......Page 262
Nature of the field equations......Page 263
Longitudinal Mach line in regions (i) and (iii)......Page 264
Jumps in strain and balance of momentum......Page 265
Stress and velocity fields......Page 267
Summary and outlook......Page 269
Acknowledgments......Page 272
Introduction......Page 277
Equilibrium of physical forces......Page 279
Equilibrium of material forces......Page 280
Vectorial and scalar J-integrals for functionally graded materials......Page 281
Spatial and material motion problem......Page 282
Material force method for J-integral evaluation......Page 284
Single edge specimen in tension......Page 285
Three point bending specimen......Page 287
Summary......Page 288
Acknowledgements......Page 289
Introduction......Page 293
Elastic body with microcracks......Page 294
Asymptotic developments homogenization......Page 295
Balance of material momentum......Page 296
Damage problem: Numerical implementation......Page 297
Numerical results......Page 299
Conclusions......Page 302
