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Analysis and Approximation of Contact Problems with Adhesion or Damage

Mircea Sofonea, Weimin Han, and Meir Shillor
Publisher: 
Chapman & Hall/CRC
Publication Date: 
2006
Number of Pages: 
220
Format: 
Hardcover
Series: 
Pure and Applied Mathematics 276
Price: 
99.95
ISBN: 
1-58488-585-8
Category: 
Monograph
We do not plan to review this book.

 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

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