Elasticity and Plasticity of Large Deformations: An Introduction

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Springer Science & Business Media, Aug 3, 2008 - Technology & Engineering - 340 pages
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This book is based on the lecture notes of courses given by the author over the last decade at the Otto-von-Guericke University of Magdeburg and the Technical University of Berlin. Since the author is concerned with researching material t- ory and, in particular, elasto-plasticity, these courses were intended to bring the students close to the frontiers of today’s knowledge in this particular field, an opportunity now offered also to the reader. The reader should be familiar with vectors and matrices, and with the basics of calculus and analysis. Concerning mechanics, the book starts right from the - ginning without assuming much knowledge of the subject. Hence, the text should be generally comprehensible to all engineers, physicists, mathematicians, and others. At the beginning of each new section, a brief Comment on the Literature c- tains recommendations for further reading. Throughout the text we quote only the important contributions to the subject matter. We are far from being complete or exhaustive in our references, and we apologise to any colleagues not mentioned in spite of their important contributions to the particular items. It is intended to indicate any corrections to this text on our website http://www.uni-magdeburg.de/ifme/l-festigkeit/elastoplasti.html along with remarks from the readers, who are encouraged to send their frank cri- cisms, comments and suggestions to bertram@mb.uni-magdeburg.de. All the author’s royalties from this issue will be donated to charitable organi- tions like Terres des Hommes.
 

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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
176
61 Reduced Elastic Forms
178
62 ThermoElasticity
179
63 Change of the Reference Placement
180
64 Elastic Isomorphy
182
65 Elastic Symmetry
185
66 Isotropic Elasticity
195
67 Incremental Elastic Laws
200

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
The Principles of Material Theory
153
42 Local Action
154
43 EUCLIDean Invariances
155
44 Extension of the Principles to Thermodynamics
159
Internal Constraints
167
52 ThermoMechanical Internal Constraints
172
68 Symmetries in ThermoElasticity
205
Hyperelasticity
209
72 Hyperelastic Materials
211
73 Hyperelastic Isomorphy and Symmetry
216
74 Isotropic Hyperelasticity
218
Solutions
228
82 Universal Solutions
236
Inelasticity
249
Plasticity
253
101 Elastic Ranges
254
102 Thermoplasticity
284
103 Viscoplasticity
291
104 Plasticity Theories with Intermediate Placements
293
105 Crystal Plasticity
303
References
316
Index
335
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Creep Mechanics
Josef Betten
Limited preview - 2008
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