Overview

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.

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9781584885856

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Reviews

“This book summarizes and completes the work of the authors on the topic of dynamic and quasistatic contact problems with adhesion or damage of viscoelastic structures in recent years. Different models involving adhesion and material damages are presented with both the theoretical result (existence and uniqueness of a weak solution) and the numerical analysis result (optimal convergence of discrete approximation by finite element methods) in a unified framework. The book is well presented and easy to read.” — Yves Renard, (Villeurbanne), in Mathematical Reviews, Issue 2007f gt; A Seminal Contribution to the Field by Renowned Researchers

This book summarizes and completes the work of the authors on the topic of dynamic and quasistatic contact problems with adhesion or damage of viscoelastic structures in recent years. Different models involving adhesion and material damages are presented with both the theoretical result (existence and uniqueness of a weak solution) and the numerical analysis result (optimal convergence of discrete approximation by finite element methods) in a unified framework. The book is well presented and easy to read. - Yves Renard, (Villeurbanne), in Mathematical Reviews, Issue 2007f gt; A Seminal Contribution to the Field by Renowned Researchers

Author Information

Mircea Sofonea, Weimin Han, Meir Shillor

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