Mathematical Models in Contact Mechanics

A complete introduction to the modelling and mathematical analysis of contact processes with deformable solids.

Mircea Sofonea (Author), Andaluzia Matei (Author)

9781107606654, Cambridge University Press

Paperback / softback, published 13 September 2012

293 pages, 5 b/w illus.
22.8 x 15.2 x 1.5 cm, 0.42 kg

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.

Preface
List of symbols
Part I. Introduction to Variational Inequalities: 1. Preliminaries on functional analysis
2. Elliptic variational inequalities
3. History-dependent variational inequalities
Part II. Modelling and Analysis of Contact Problems: 4. Modelling of contact problems
5. Analysis of elastic contact problems
6. Analysis of elastic-visco-plastic contact problems
7. Analysis of piezoelectric contact problems
Bibliographical notes
References
Index.

Subject Areas: Mechanics of solids [TGMD], Mathematical physics [PHU], Dynamics & statics [PHDT], Fluid mechanics [PHDF]