1st Edition
Analysis and Approximation of Contact Problems with Adhesion or Damage
238 Pages
by
Chapman & Hall
220 Pages
by
Chapman & Hall
Also available as eBook on:
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... Read more
Preface
List of Symbols
Modeling and Mathematical Background
Basic Equations and Boundary Conditions
Physical Setting and Evolution Equations
Boundary Conditions
Contact Processes with Adhesion
Constitutive Equations with Damage
Preliminaries on Functional Analysis
Function Spaces and Their Properties
Elements of Nonlinear Analysis
Standard Results on Variational Inequalities and Evolution Equations
Elementary Inequalities
Preliminaries on Numerical Analysis
Finite Difference and Finite Element Discretizations
Approximation of Displacements and Velocities
Estimates on the Discretization of Adhesion Evolution
Estimates on the Discretization of Damage Evolution
Estimates on the Discretization of Viscoelastic Constitutive Law
Estimates on the Discretization of Viscoplastic Constitutive Law
Frictionless Contact Problems with Adhesion
Quasistatic Viscoelastic Contact with Adhesion
Problem Statement
Existence and uniqueness
Continuous Dependence on the Data
Spatially Semidiscrete Numerical Approximation
Fully Discrete Numerical Approximation
Dynamic Viscoelastic Contact with Adhesion
Problem Statement
Existence and Uniqueness
Fully Discrete Numerical Approximation
Quasistatic Viscoplastic Contact with Adhesion
Problem Statement
Existence and Uniqueness for the Signorini Problem
Numerical Approximation for the Signorini Problem
Existence and Uniqueness for the Problem with Normal Compliance
Numerical Approximation of the Problem with Normal Compliance
Relation between the Signorini and Normal Compliance Problems
Contact Problems with Damage
Quasistatic Viscoelastic Contact with Damage
Problem Statement
Existence and Uniqueness
Fully Discrete Numerical Approximation
Dynamic Viscoelastic Contact with Damage
Problem Statement
Existence and Uniqueness
Fully Discrete Numerical Approximation
Quasistatic Viscoplastic Contact with Damage
Problem Statement
Existence and Uniqueness for the Signorini Problem
Numerical Approximation for the Signorini Problem
Existence and Uniqueness for the Problem with Normal Compliance
Numerical Approximation of the Problem with Normal Compliance
Relation between the Signorini and Normal Compliance Problems
Notes, Comments, and Conclusions
Bibliographical Notes, Problems for Future Research, and Conclusions
Bibliographical Notes
Problems for Future Research
Conclusions
References
Index
List of Symbols
Modeling and Mathematical Background
Basic Equations and Boundary Conditions
Physical Setting and Evolution Equations
Boundary Conditions
Contact Processes with Adhesion
Constitutive Equations with Damage
Preliminaries on Functional Analysis
Function Spaces and Their Properties
Elements of Nonlinear Analysis
Standard Results on Variational Inequalities and Evolution Equations
Elementary Inequalities
Preliminaries on Numerical Analysis
Finite Difference and Finite Element Discretizations
Approximation of Displacements and Velocities
Estimates on the Discretization of Adhesion Evolution
Estimates on the Discretization of Damage Evolution
Estimates on the Discretization of Viscoelastic Constitutive Law
Estimates on the Discretization of Viscoplastic Constitutive Law
Frictionless Contact Problems with Adhesion
Quasistatic Viscoelastic Contact with Adhesion
Problem Statement
Existence and uniqueness
Continuous Dependence on the Data
Spatially Semidiscrete Numerical Approximation
Fully Discrete Numerical Approximation
Dynamic Viscoelastic Contact with Adhesion
Problem Statement
Existence and Uniqueness
Fully Discrete Numerical Approximation
Quasistatic Viscoplastic Contact with Adhesion
Problem Statement
Existence and Uniqueness for the Signorini Problem
Numerical Approximation for the Signorini Problem
Existence and Uniqueness for the Problem with Normal Compliance
Numerical Approximation of the Problem with Normal Compliance
Relation between the Signorini and Normal Compliance Problems
Contact Problems with Damage
Quasistatic Viscoelastic Contact with Damage
Problem Statement
Existence and Uniqueness
Fully Discrete Numerical Approximation
Dynamic Viscoelastic Contact with Damage
Problem Statement
Existence and Uniqueness
Fully Discrete Numerical Approximation
Quasistatic Viscoplastic Contact with Damage
Problem Statement
Existence and Uniqueness for the Signorini Problem
Numerical Approximation for the Signorini Problem
Existence and Uniqueness for the Problem with Normal Compliance
Numerical Approximation of the Problem with Normal Compliance
Relation between the Signorini and Normal Compliance Problems
Notes, Comments, and Conclusions
Bibliographical Notes, Problems for Future Research, and Conclusions
Bibliographical Notes
Problems for Future Research
Conclusions
References
Index
Biography
Mircea Sofonea, Weimin Han, Meir Shillor
“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
