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Materials with Memory

Initial-Boundary Value Problems for Constitutive Equations with Internal Variables

  • Book
  • © 1998

Overview

Authors:
  1. Hans-Dieter Alber
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1682)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-X
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  2. Introduction

    • Hans-Dieter Alber
    Pages 1-5

  3. Initial-boundary value problems for the inelastic behavior of metals

    • Hans-Dieter Alber
    Pages 7-22

  4. Constitutive equations of monotone type and generalized standard materials

    • Hans-Dieter Alber
    Pages 23-44

  5. Existence of solutions for constitutive equations of monotone type

    • Hans-Dieter Alber
    Pages 45-56

  6. Transformation of interior variables

    • Hans-Dieter Alber
    Pages 57-73

  7. Classification conditions

    • Hans-Dieter Alber
    Pages 75-97

  8. Transformation of rate independent constitutive equations

    • Hans-Dieter Alber
    Pages 99-116

  9. Application of the theory to engineering models

    • Hans-Dieter Alber
    Pages 117-136

  10. Open problems and related results

    • Hans-Dieter Alber
    Pages 137-142

  11. Back Matter

    Pages 143-166
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Keywords

About this book

This book contributes to the mathematical theory of systems of differential equations consisting of the partial differential equations resulting from conservation of mass and momentum, and of constitutive equations with internal variables. The investigations are guided by the objective of proving existence and uniqueness, and are based on the idea of transforming the internal variables and the constitutive equations. A larger number of constitutive equations from the engineering sciences are presented. The book is therefore suitable not only for specialists, but also for mathematicians seeking for an introduction in the field, and for engineers with a sound mathematical background.

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