Elasticity and Plasticity of Large Deformations: An Introduction

by Bertram, Albrecht

• ISBN13: 9783540693994
• ISBN10: 3540693998
• eBook ISBN(s): 9783540694007
• Edition: 2nd
• Format: Paperback
• Copyright: 2008-10-04
• Publisher: Springer Verlag
• More Book Details
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Summary

"The valuable input of students and colleagues has enabled the author to make many improvements to the first edition of this book, without, however, changing the main structure of the book." "As a result, the second edition "Elasticity and Plasticity of Large deformations" still offers a careful introduction to modern non linear mechanics. It presents in detail the used mathematical tools, such as tensor algebra and analysis. The general theory of mechanical behavior is particularized for the broad and important classes of elasticity and plasticity. The book 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."--BOOK JACKET.

Table of Contents

List of Frequently Used Symbols	p. XI
List of Selected Scientists	p. XVII
Introduction	p. 1
Mathematical Preparation	p. 3
Repetitions from Vector Algebra	p. 5
Tensor Algebra	p. 10
Tensor Product and Tensor Components	p. 17
The Eigenvalue Problem	p. 21
Special Tensors	p. 29
Tensors of Higher Order	p. 35
Isotropic Tensor Functions	p. 46
Tensor Analysis	p. 53
The EUCLIDean Point Space	p. 71
The Covariant Derivative	p. 76
Integral Theorems	p. 87
Kinematics	p. 91
Placements of Bodies	p. 91
Time Derivatives	p. 94
Spatial Derivatives	p. 95
Balance Laws	p. 121
Mass	p. 121
The General Balance Equation	p. 122
Observer-Dependent Laws of Motion	p. 130
Stress Analysis	p. 136
The Thermodynamical Balances	p. 149
The Principles of Material Theory	p. 153
Determinism	p. 153
Local Action	p. 154
EUCLIDean Invariances	p. 155
Extension of the Principles to Thermodynamics	p. 159
Internal Constraints	p. 167
Mechanical Internal Constraints	p. 167
Thermo-Mechanical Internal Constraints	p. 172
Elasticity	p. 177
Reduced Elastic Forms	p. 178
Thermo-Elasticity	p. 179
Change of the Reference Placement	p. 180
Elastic Isomorphy	p. 182
Elastic Symmetry	p. 185
Isotropic Elasticity	p. 195
Incremental Elastic Laws	p. 200
Symmetries in Thermo-Elasticity	p. 205
Hyperelasticity	p. 209
Thermodynamical Restrictions	p. 209
Hyperelastic Materials	p. 211
Hyperelastic Isomorphy and Symmetry	p. 216
Isotropic Hyperelasticity	p. 218
Solutions	p. 229
Boundary Value Problems	p. 229
Universal Solutions	p. 236
Inelasticity	p. 249
Plasticity	p. 253
Elastic Ranges	p. 254
Thermoplasticity	p. 284
Viscoplasticity	p. 291
Plasticity Theories with Intermediate Placements	p. 293
Crystal Plasticity	p. 303
References	p. 317
Index	p. 335
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