Analysis and Approximation of Contact Problems with Adhesion or Damage

by Sofonea; Mircea

• ISBN13: 9781584885856
• ISBN10: 1584885858
• Format: Hardcover
• Copyright: 2005-09-26
• Publisher: Chapman & Hall/

Summary

Research into contact problems continues to produce a rapidly growing body of knowledge. Recognizing the need for a single, concise source of information on models and analysis of contact problems, accomplished experts Sofonea, Han, and Shillor carefully selected several models and thoroughly study them in Analysis and Approximation of Contact Problems with Adhesion or Damage. The book describes very recent models of contact processes with adhesion or damage along with their mathematical formulations, variational analysis, and numerical analysis.Following an introduction to modeling and functional and numerical analysis, the book devotes individual chapters to models involving adhesion and material damage, respectively, with each chapter exploring a particular model. For each model, the authors provide a variational formulation and establish the existence and uniqueness of a weak solution. They study a fully discrete approximation scheme that uses the finite element method to discretize the spatial domain and finite differences for the time derivatives. The final chapter summarizes the results, presents bibliographic comments, and considers future directions in the field.Employing recent results on elliptic and evolutionary variational inequalities, convex analysis, nonlinear equations with monotone operators, and fixed points of operators, Analysis and Approximation of Contact Problems with Adhesion or Damage places these important tools and results at your fingertips in a unified, accessible reference.

Author Biography

Meir Shillor is Professor of Mathematical Sciences at Oakland University, Rochester, Michigan, USA.

Table of Contents

Modeling and mathematical background	p. 1
Basic equations and boundary conditions	p. 3
Preliminaries on functional analysis	p. 25
Preliminaries on numerical analysis	p. 51
Frictionless contact problems with adhesion	p. 79
Quasistatic viscoelastic contact with adhesion	p. 81
Dynamic viscoelastic contact with adhesion	p. 103
Quasistatic viscoplastic contact with adhesion	p. 117
Contact problems with damage	p. 147
Quasistatic viscoelastic contact with damage	p. 149
Dynamic viscoelastic contact with damage	p. 163
Quasistatic viscoplastic contact with damage	p. 173
Notes, comments, and conclusions	p. 193
Bibliographical notes, problems for future research, and conclusions	p. 195
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