## Elasticity and Plasticity of Large Deformations: An IntroductionThis 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

3 | |

5 | |

10 | |

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 |

316 | |

335 | |

### Other editions - View all

Elasticity and Plasticity of Large Deformations: An Introduction Albrecht Bertram Limited preview - 2011 |

Elasticity and Plasticity of Large Deformations: an introduction Albrecht Bertram Limited preview - 2005 |

Elasticity and Plasticity of Large Deformations: An Introduction Albrecht Bertram Limited preview - 2007 |

### Common terms and phrases

2nd-order tensors arbitrary assume body called CAUCHY stresses CAUCHY´s CLAUSIUS-DUHEM inequality components condition constant COOS current placement decomposition deformation gradient depend derivative determined deviatoric differential eigenvalues eigenvectors Elap elastic law elastic ranges equation equivalent stress EUCLIDean transformations EULERean finite grad hardening rule holds hyperelastic inner product internal constraints Inv+ invertible isomorphic isotropic isotropic tensor function linear mapping mass density material functional material point material stress tensor motion obtain orthogonal PISM polar decomposition principal invariants principle Psym reduced form reference placement representation respect rotation shear simple shear skew slip systems space spatial strain tensor symmetric tensors symmetry group symmetry transformations T1PK T2PK tensor field tetrad Theorem theory thermo-elastic thermo-kinematical process tion variables vector field velocity wF(F yield criterion yield limit zero