## Elasticity and Plasticity of Large Deformations: an introductionThe 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 |

322 | |

### 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 - 2008 |

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

### Common terms and phrases

2nd-order tensors 4th-order ansatz arbitrary assume basis BERTRAM called CAUCHY stresses CAUCHY-GREEN tensor CLAUSIUS-DUHEM inequality components consider COOS current elastic current placement decomposition deformation gradient depend derivative determined deviatoric differential eigenvalues eigenvectors elastic law elastic materials elastic ranges equation EUCLIDean space EUCLIDean transformations EULERean generalised grad hardening rule heat flux holds hyperelastic inner product internal constraints invertible isomorphic isotropic isotropic tensor function mass density material functional material point material stress tensor material theory mechanics NAGHDI NOLL notation obtain PISM plastic transformation principal invariants principle reduced form reference placement representation respect rotation simple shear skew slip systems spatial stiffness tetrad strain energy strain tensor subsymmetries symmetric tensors symmetry group symmetry transformations T2PK tensor field Theorem thermo-elastic thermo-kinematical process thermodynamics tion unimodular unique universal solutions variables vector field velocity yield criterion yield limit zero