Beschreibung
Inhaltsangabe>1 Introduction 1 > >2 Initial-Boundary Value Problems for the Inelastic Behavior of > Metals 7 >2.1 Formulation of the Initial-Boundary Value Problems.7 >2.2 Examples of Constitutive Equations.11 > >3 Constitutive Equations of Monotone Type and Generalized > Standard Materials 23 >3.1 Energy Estimate and Classes of Constitutive Equations.23 >3.2 Uniqueness and Existence for Dynamic and Quasi-Static Problems: > Basic Ideas of the Proofs and Results in the Literature.27 >3.3 Examples of Constitutive Equations Revisited.31 >3.4 A Criterion for Monotone Type.41 > >4 Existence of Solutions for Constitutive Equations of Monotone > Type 45 >4.1 Formulation of the Problem as a First Order Evolution Equation.45 >4.2 Maximality of the Evolution Operator.48 >4.3 Existence for the Dynamic Problem.56 > >5 Transformation of Interior Variables 57 >5.1 Transformation Fields.57 >5.2 Properties of the Transformation: Restrictions Imposed by > the e-Independence of the Transformation Field > and Invariance under Linear Transformations.60 >5.3 The Class of Constitutive Equations Transformable to Monotone > Type. >5.4 The Class of Constitutive Equations Transformable to Gradient > Type. >5.5 The Class of Constitutive Equations Transformable to Monotone- > Gradient Type.69 > >6 Classification Conditions 75 >6.1 Transformations which Leave the Class of Pre-Monotone > Equations Invariant.76 >6.2 Transformation of Pre-Monotone Equations to Gradient Type.87 > >7 Transformation of Rate Independent Constitutive Equations 99 >7.1 Transformationof Constitutive Equations Containing Set-Valued > Operators. >7.2 Transformation to Monotone-Gradient Type.102 >7.3 Example 1: One Variable of Isotropic Hardening.106 >7.4 Example 2: Several Variables of Isotropic Hardening.111 > >8 Application of the Theory to Engineering Models 117 >8.1 Pre-Monotone Type of the Model.117 >8.2 Conditions for Monotone Type of the Model.119 >8.3 Pre-Monotone Type Preserving Transformations of the Model.125 >8.4 Transformation to Gradient Type.126 >8.5 Transformation to Monotone Type and to Monotone-Gradient > Type. > >9 Open Problems and Related Results 137 >9.1 Transformation Fields Depending on e and z.137 >9.2 History Functionals.138 >9.3 Hysteresis Operators. Existence Theory in L.139 >9.4 Constitutive Equations Defining Continuous Operators in > Banach Spaces.14 > >A The Second Law of Thermodynamics and the Dissipation > Inequality 143 >A.1 Consequences of the Second Law for the Constitutive Equations.143 >A.2 The Free Energy.149 > >Bibliography 153 > >Index 165 >
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