Elasticity and Plasticity of Large Deformations: an introduction

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Springer Science & Business Media, 2005 - Technology & Engineering - 326 pages
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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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Contents

Mathematical Preparation
3
11 Repetitions from Vector Algebra
5
12 Tensor Algebra
10
121 Tensor Product and Tensor Components
17
122 The Eigenvalue Problem
21
123 Special Tensors Skew Tensors
29
124 Tensors of Higher Order
35
125 Isotropic Tensor Functions
46
Elasticity
175
61 Reduced Elastic Forms
176
62 ThermoElasticity
177
63 Change of the Reference Placement
178
64 Elastic Isomorphy
180
65 Elastic Symmetry
183
66 Isotropic Elasticity
193
67 Incremental Elastic Laws
198

13 Tensor Analysis
53
14 The EUCLIDean Point Space
71
141 The Covariant Derivative
76
142 Integral Theorems
87
Kinematics
91
22 Time Derivatives
94
23 Spatial Derivatives
95
Balance Laws
121
32 The General Balance Equation
122
33 ObserverDependent Laws of Motion
130
34 Stress Analysis
136
35 The Thermodynamical Balances
149
4 The Principles of Material Theory
153
42 Local Action
154
43 EUCLIDean Invariances
155
44 Extension of the Principles to Thermodynamics
159
5 Internal Constraints
166
52 ThermoMechanical Internal Constraints
171
68 Symmetries in ThermoEIasticity
203
Hyperelasticity
206
72 Hyperelastic Materials
208
73 Hyperelastic Isomorphy and Symmetry
213
74 Isotropic Hyperelasticity
215
Solutions
225
82 Universal Solutions
232
Inelasticity
244
Plasticity
248
101 Elastic Ranges
249
102 Thertnoplasticity
275
103 Viscoplasticity
282
104 Plasticity Theories with Intermediate Placements
284
105 Crystal Plasticity
294
References
307
Index
322
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Creep Mechanics
Josef Betten
Limited preview - 2008
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