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Phase Separation Coupled with Damage Processes

Analysis of Phase Field Models in Elastic Media

  • Christian Heinemann
  • Christiane Kraus

Table of contents

  1. Front Matter
    Pages i-xii
  2. Christian Heinemann, Christiane Kraus
    Pages 1-7
  3. Christian Heinemann, Christiane Kraus
    Pages 9-34
  4. Christian Heinemann, Christiane Kraus
    Pages 35-50
  5. Christian Heinemann, Christiane Kraus
    Pages 119-143
  6. Christian Heinemann, Christiane Kraus
    Pages 163-165
  7. Back Matter
    Pages 167-173

About this book

Introduction

The authors explore a unifying model which couples phase separation and damage processes in a system of partial differential equations. The model has technological applications to solder materials where interactions of both phenomena have been observed and cannot be neglected for a realistic description. The equations are derived in a thermodynamically consistent framework and suitable weak formulations for various types of this coupled system are presented. In the main part, existence of weak solutions is proven and degenerate limits are investigated.

Contents

  • Modeling of Phase Separation and Damage Processes
  • Notion of Weak Solutions
  • Existence of Weak Solutions
  • Degenerate Limit

Target Groups

  • Researchers, academics and scholars in the field of (applied) mathematics
  • Material scientists in the field of modeling damaging processes

The Authors

Christian Heinemann earned his doctoral degree at the Humboldt-Universität zu Berlin under the supervision of Prof. Dr. Jürgen Sprekels and Dr. Christiane Kraus. He is a member of the research staff at the Young Scientists' Group at the Weierstrass Institute for Applied Analysis and Stochastics in Berlin.

Christiane Kraus is a leader of the Young Scientists' Group at the Weierstrass Institute for Applied Analysis and Stochastics in Berlin.

Keywords

Cahn-Hilliard equations Damage Processes Doubly Nonlinear Differential Inclusions Existence of Weak Solutions Field Models in Elastic Media Modeling of Phase Separation

Authors and affiliations

  • Christian Heinemann
    • 1
  • Christiane Kraus
    • 2
  1. 1.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany
  2. 2.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany

Bibliographic information

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