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Mathematical models in contact mechanics

Author: Mircea Sofonea; Andaluzia Matei
Publisher: New York : Cambridge University Press, 2012.
Series: London Mathematical Society lecture note series, 398.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"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
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Document Type: Book
All Authors / Contributors: Mircea Sofonea; Andaluzia Matei
ISBN: 9781107606654 1107606659
OCLC Number: 793221739
Description: xiv, 280 pages : illustrations ; 24 cm.
Contents: Preliminaries on functional analysis --
Elliptic variational inequalities --
History-dependent variational inequalities --
Modelling of contact problems --
Analysis of elastic contact problems --
Analysis of elastic-visco plastic contact problems --
Analysis of piezoelectric contact problems.
Series Title: London Mathematical Society lecture note series, 398.
Responsibility: M. Sofonea, A. Matei.
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Abstract:

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

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   schema:description ""Contact processes between deformable bodies abound in industry and everyday life and, for this reason, considerable efforts have been made in their modelling and analysis. Owing to their inherent complexity, contact phenomena lead to new and interesting mathematical models. Here and everywhere in this book by a mathematical model we mean a system of partial differential equations, associated with boundary conditions and initial conditions, eventually, which describes a specific contact process. The purpose of this book is to introduce the reader to some representative mathematical models which arise in Contact Mechanics. Our aim is twofold: first, to present a sound and rigorous description of the way in which the mathematical models are constructed; second, to present the mathematical analysis of such models which includes the variational formulation, existence, uniqueness and convergence results. To this end, we use results on various classes of variational inequalities in Hilbert spaces, that we present in an abstract functional framework. Also, we use various functional methods, including monotonicity, compactness, penalization, regularization and duality methods. Moreover, we pay particular attention to the mechanical interpretation of our results and, in this way, we illustrate the cross fertilization between modelling and applications on the one hand, and nonlinear analysis on the other hand"--"@en ;
   schema:description ""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"--"@en ;
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