Analysis and Approximation of Contact Problems with Adhesion or Damage

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.

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.

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