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Zusatztext "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 Informationen zum Autor Mircea Sofonea, Weimin Han, Meir Shillor Klappentext Beginning with an introduction to modeling and functional and numerical analysis! Analysis and Approximation of Contact Problems with Adhesion or Damage devotes individual chapters to models involving adhesion and material damage! with each chapter exploring a particular model. For each model! the authors provide the 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 section summarizes the results! presents bibliographic comments! and considers future directions in the field. Zusammenfassung Beginning with an introduction to modeling and functional and numerical analysis, this title deals with the chapters to models involving adhesion and material damage, exploring a particular model. For various models, it provides a variational formulation and establishes the existence and uniqueness of a weak solution. Inhaltsverzeichnis 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 a...
