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This book is motivated by stimulating problems in contact mechanics, emphasizing antiplane frictional contact with linearly elastic and viscoelastic materials. It focuses on the essentials with respect to the qualitative aspects of several classes of variational inequalities (VIs). Clearly presented, easy to follow, and well-referenced, this work treats almost entirely VIs of the second kind, with much of the material being state-of-the-art. Applied mathematicians and advanced graduate students wishing to enter the field of VIs would benefit from this work as it sets out in detail basic features and results in the mathematical theory of contact mechanics. Researchers interested in applications of numerical analysis pertaining to VIs would also find the work useful. Assuming a reasonable knowledge of functional analysis, this volume is a must for graduate students, practitioners, and engineers engaged in contact mechanics.

Variational inequalities (Mathematics). --- Variational inequalities (Mathematics) --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Differential inequalities. --- Inequalities, Variational (Mathematics) --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Operator theory. --- Partial differential equations. --- Calculus of variations. --- Continuum mechanics. --- Calculus of Variations and Optimal Control; Optimization. --- Analysis. --- Continuum Mechanics and Mechanics of Materials. --- Global Analysis and Analysis on Manifolds. --- Operator Theory. --- Partial Differential Equations. --- Mechanics of continua --- Elasticity --- Mechanics, Analytic --- Field theory (Physics) --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Partial differential equations --- Functional analysis --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- 517.1 Mathematical analysis --- Mathematical analysis --- Math --- Science --- Inequalities (Mathematics) --- Calculus of variations --- Differential inequalities --- Mathematical optimization. --- Mechanics. --- Mechanics, Applied. --- Global analysis. --- Differential equations, partial. --- Solid Mechanics. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Operations research --- Simulation methods --- System analysis --- Calculus. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Functions --- Geometry, Infinitesimal

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This text provides a complete introduction to the theory of variational inequalities with emphasis on contact mechanics. It covers existence, uniqueness and convergence results for variational inequalities, including the modelling and variational analysis of specific frictional contact problems with elastic, viscoelastic and viscoplastic materials. New models of contact are presented, including contact of piezoelectric materials. Particular attention is paid to the study of history-dependent quasivariational inequalities and to their applications in the study of contact problems with unilateral constraints. The book fully illustrates the cross-fertilisation between modelling and applications on the one hand and nonlinear mathematical analysis on the other. Indeed, the reader will gain an understanding of how new and nonstandard models in contact mechanics lead to new types of variational inequalities and, conversely, how abstract results concerning variational inequalities can be applied to prove the unique solvability of the corresponding contact problems.

Contact mechanics --- Mathematical models. --- Mechanics, Applied