Elasticity and plasticity of large deformations: an introduction

Albrecht Bertram9783540240334, 3540240330

The book offers a careful introduction to modern non-linear mechanics. The used mathematical tools, such as tensor algebra and analysis are given in detail. The general theory of mechanical behaviour is particularized for the broad and important classes of elasticity and plasticity. It is intended to bring the reader close to the fields of today’s research activities. A list of notations and an index help the reader to find specific topics. The book is based on three decades of teaching experience in this field.

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Table of contents :
Contents……Page 6
List of Frequently Used Symbols……Page 8
List of Selected Scientists……Page 13
Introduction……Page 15
1 Mathematical Preparation……Page 17
1.1 Repetitions from Vector Algebra……Page 19
1.2 Tensor Algebra……Page 24
1.2.1 Tensor Product and Tensor Components……Page 31
1.2.2 The Eigenvalue Problem……Page 35
1.2.3 Special Tensors……Page 43
1.2.4 Tensors of Higher Order……Page 49
1.2.5 Isotropic Tensor Functions……Page 60
1.3 Tensor Analysis……Page 67
1.4 The EUCLIDean Point Space……Page 85
1.4.1 The Covariant Derivative……Page 90
1.4.2 Integral Theorems……Page 101
2.1 Placements of Bodies……Page 105
2.2 Time Derivatives……Page 108
2.3 Spatial Derivatives……Page 109
3.1 Mass……Page 135
3.2 The General Balance Equation……Page 136
3.3 Observer-Dependent Laws of Motion……Page 144
3.4 Stress Analysis……Page 150
3.5 The Thermodynamical Balances……Page 163
4.1 Determinism……Page 167
4.2 Local Action……Page 168
4.3 EUCLIDean Invariances……Page 169
4.4 Extension of the Principles to Thermodynamics……Page 173
5.1 Mechanical Internal Constraints……Page 180
5.2 Thermo-Mechanical Internal Constraints……Page 185
6 Elasticity……Page 189
6.1 Reduced Elastic Forms……Page 190
6.2 Thermo-Elasticity……Page 191
6.3 Change of the Reference Placement……Page 192
6.4 Elastic Isomorphy……Page 194
6.5 Elastic Symmetry……Page 197
6.6 Isotropic Elasticity……Page 207
6.7 Incremental Elastic Laws……Page 212
6.8 Symmetries in Thermo-Elasticity……Page 217
7.1 Thermodynamical Restrictions……Page 220
7.2 Hyperelastic Materials……Page 222
7.3 Hyperelastic Isomorphy and Symmetry……Page 227
7.4 Isotropic Hyperelasticity……Page 229
8.1 Boundary Value Problems……Page 239
8.2 Universal Solutions……Page 246
9 Inelasticity……Page 258
10 Plasticity……Page 262
10.1 Elastic Ranges……Page 263
10.2 Thermoplasticity……Page 289
10.3 Viscoplasticity……Page 296
10.4 Plasticity Theories with Intermediate Placements……Page 298
10.5 Crystal Plasticity……Page 308
References……Page 321
D……Page 336
I……Page 337
P……Page 338
S……Page 339
Z……Page 340