Elasticity And Plasticity Of Large Deformations

by Bertram, Albrecht

• ISBN13: 9783540240334
• ISBN10: 3540240330
• eBook ISBN(s): 9783540275251
• Format: Hardcover
• Copyright: 2005-07-31
• Publisher: Springer Verlag
• More Book Details
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Summary

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.

Table of Contents

List of Frequently Used Symbols	viii
List of Selected Scientists	xiii
Introduction	1	(247)
1 Mathematical Preparation	3	(88)
1.1 Repetitions from Vector Algebra	5	(5)
1.2 Tensor Algebra	10	(43)
1.2.1 Tensor Product and Tensor Components	17	(4)
1.2.2 The Eigenvalue Problem	21	(8)
1.2.3 Special Tensors	29	(6)
1.2.4 Tensors of Higher Order	35	(11)
1.2.5 Isotropic Tensor Functions	46	(7)
1.3 Tensor Analysis	53	(18)
1.4 The EUCLIDean Point Space	71	(20)
1.4.1 The Covariant Derivative	76	(11)
1.4.2 Integral Theorems	87	(4)
2 Kinematics	91	(30)
2.1 Placements of Bodies	91	(3)
2.2 Time Derivatives	94	(1)
2.3 Spatial Derivatives	95	(26)
3 Balance Laws	121	(32)
3.1 Mass	121	(1)
3.2 The General Balance Equation	122	(8)
3.3 Observer-Dependent Laws of Motion	130	(6)
3.4 Stress Analysis	136	(13)
3.5 The Thermodynamical Balances	149	(4)
4 The Principles of Material Theory	153	(13)
4.1 Determinism	153	(1)
4.2 Local Action	154	(1)
4.3 EUCLIDean Invariances	155	(4)
4.4 Extension of the Principles to Thermodynamics	159	(7)
5 Internal Constraints	166	(9)
5.1 Mechanical Internal Constraints	166	(5)
5.2 Thermo-Mechanical Internal Constraints	171	(4)
6 Elasticity	175	(31)
6.1 Reduced Elastic Forms	176	(1)
6.2 Thermo-Elasticity	177	(1)
6.3 Change of the Reference Placement	178	(2)
6.4 Elastic Isomorphy	180	(3)
6.5 Elastic Symmetry	183	(10)
6.6 Isotropic Elasticity	193	(5)
6.7 Incremental Elastic Laws	198	(5)
6.8 Symmetries in Thermo-Elasticity	203	(3)
7 Hyperelasticity	206	(19)
7.1 Thermodynamical Restrictions	206	(2)
7.2 Hyperelastic Materials	208	(5)
7.3 Hyperelastic Isomorphy and Symmetry	213	(2)
7.4 Isotropic Hyperelasticity	215	(10)
8 Solutions	225	(19)
8.1 Boundary Value Problems	225	(7)
8.2 Universal Solutions	232	(12)
9 Inelasticity	244	(4)
10 Plasticity	248	(59)
10.1 Elastic Ranges	249	(26)
10.2 Thermoplasticity	275	(7)
10.3 Viscoplasticity	282	(2)
10.4 Plasticity Theories with Intermediate Placements	284	(10)
10.5 Crystal Plasticity	294	(13)
References	307	(15)
Index	322