List of Frequently Used Symbols ................................ XI
List of Selected Scientists .................................. XVII
Introduction .................................................... 1
1 Mathematical Preparation ..................................... 3
1.1 Repetitions from Vector Algebra ......................... 5
1.2 Tensor Algebra ......................................... 10
1.2.1 Tensor Product and Tensor Components ............ 17
1.2.2 The Eigenvalue Problem .......................... 21
1.2.3 Special Tensors ................................. 29
1.2.4 Tensors of Higher Order ......................... 35
1.2.5 Isotropic Tensor-Functions ...................... 46
1.3 Tensor Analysis ........................................ 53
1.4 The EUCLIDean Point Space .............................. 71
1.4.1 The Covariant Derivative ........................ 76
1.4.2 Integral Theorems ............................... 87
2 Kinematics .................................................. 91
2.1 Placements of Bodies ................................... 91
2.2 Time Derivatives ....................................... 94
2.3 Spatial Derivatives .................................... 95
3 Balance Laws ............................................... 121
3.1 Mass .................................................. 121
3.2 The General Balance Equation .......................... 122
3.3 Observer-Dependent Laws of Motion ..................... 130
3.4 Stress Analysis ....................................... 136
3.5 The Thermodynamical Balances .......................... 149
4 The Principles of Material Theory .......................... 153
4.1 Determinism ........................................... 153
4.2 Local Action .......................................... 154
4.3 EUCLIDean Invariances ................................. 155
4.4 Extension of the Principles to Thermodynamics ......... 159
5 Internal Constraints ....................................... 167
5.1 Mechanical Internal Constraints ....................... 167
5.2 Thermo-Mechanical Internal Constraints ................ 172
6 Elasticity ................................................. 177
6.1 Reduced Elastic Forms ................................. 178
6.2 Thermo-Elasticity ..................................... 179
6.3 Change of the Reference Placement ..................... 180
6.4 Elastic Isomorphy ..................................... 182
6.5 Elastic Symmetry ...................................... 185
6.6 Isotropic Elasticity .................................. 195
6.7 Incremental Elastic Laws .............................. 200
6.8 Symmetries in Thermo-Elasticity ....................... 205
7 Hyperelasticity ............................................ 209
7.1 Thermodynamical Restrictions .......................... 209
7.2 Hyperelastic Materials ................................ 211
7.3 Hyperelastic Isomorphy and Symmetry ................... 216
7.4 Isotropic Hyperelasticity ............................. 218
8 Solutions .................................................. 231
8.1 Boundary Value Problems ............................... 231
8.2 Universal Solutions ................................... 238
9 Inelasticity ............................................... 251
10 Plasticity ................................................. 255
10.1 Elastic Ranges ........................................ 256
10.2 Thermoplasticity ...................................... 286
10.3 Viscoplasticity ....................................... 293
10.4 Plasticity Theories with Intermediate Placements ...... 296
10.5 Crystal Plasticity .................................... 306
10.6 Material Plasticity ................................... 319
References .................................................... 321
Index ......................................................... 341
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