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1 | (6) |
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2 Initial-Boundary Value Problems for the Inelastic Behavior of Metals |
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7 | (16) |
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2.1 Formulation of the Initial-Boundary Value Problems |
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7 | (4) |
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2.2 Examples of Constitutive Equations |
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11 | (12) |
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3 Constitutive Equations of Monotone Type and Generalized Standard Materials |
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23 | (22) |
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3.1 Energy Estimate and Classes of Constitutive Equations |
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23 | (4) |
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3.2 Uniqueness and Existence for Dynamic and Quasi-Static Problems: Basic Ideas of the Proofs and Results in the Literature |
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27 | (4) |
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3.3 Examples of Constitutive Equations Revisited |
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31 | (10) |
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3.4 A Criterion for Monotone Type |
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41 | (4) |
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4 Existence of Solutions for Constitutive Equations of Monotone Type |
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45 | (12) |
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4.1 Formulation of the Problem as a First Order Evolution Equation |
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45 | (3) |
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4.2 Maximality of the Evolution Operator |
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48 | (8) |
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4.3 Existence for the Dynamic Problem |
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56 | (1) |
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5 Transformation of Interior Variables |
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57 | (18) |
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5.1 Transformation Fields |
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57 | (3) |
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5.2 Properties of the Transformation: Restrictions Imposed by the Epsilon-Independence of the Transformation Field and Invariance under Linear Transformations |
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60 | (5) |
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5.3 The Class of Constitutive Equations Transformable to Monotone Type |
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65 | (2) |
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5.4 The Class of Constitutive Equations Transformable to Gradient Type |
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67 | (2) |
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5.5 The Class of Constitutive Equations Transformable to Monotone-Gradient Type |
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69 | (6) |
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6 Classification Conditions |
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75 | (24) |
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6.1 Transformations which Leave the Class of Pre-Monotone Equations Invariant |
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76 | (11) |
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6.2 Transformation of Pre-Monotone Equations to Gradient Type |
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87 | (12) |
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7 Transformation of Rate Independent Constitutive Equations |
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99 | (18) |
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7.1 Transformation of Constitutive Equations Containing Set-Valued Operators |
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99 | (3) |
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7.2 Transformation to Monotone-Gradient Type |
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102 | (4) |
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7.3 Example 1: One Variable of Isotropic Hardening |
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106 | (5) |
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7.4 Example 2: Several Variables of Isotropic Hardening |
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111 | (6) |
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8 Application of the Theory to Engineering Models |
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117 | (20) |
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8.1 Pre-Monotone Type of the Model |
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117 | (2) |
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8.2 Conditions for Monotone Type of the Model |
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119 | (6) |
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8.3 Pre-Monotone Type Preserving Transformations of the Model |
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125 | (1) |
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8.4 Transformation to Gradient Type |
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126 | (3) |
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8.5 Transformation to Monotone Type and to Monotone-Gradient Type |
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129 | (8) |
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9 Open Problems and Related Results |
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137 | (6) |
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9.1 Transformation Fields Depending on Epsilon and Zeta |
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137 | (1) |
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138 | (1) |
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9.3 Hysteresis Operators. Existence Theory in L(p) |
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139 | (3) |
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9.4 Constitutive Equations Defining Continuous Operators in Banach Spaces |
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142 | (1) |
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A The Second Law of Thermodynamics and the Dissipation Inequality |
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143 | (10) |
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A.1 Consequences of the Second Law for the Constitutive Equations |
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143 | (6) |
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149 | (4) |
| Bibliography |
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153 | (12) |
| Index |
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165 | |
