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An analytical and numerical approach to a bilateral contact problem with nonmonotone friction

Mikaël BarboteuKrzysztof BartoszPiotr Kalita — 2013

International Journal of Applied Mathematics and Computer Science

We consider a mathematical model which describes the contact between a linearly elastic body and an obstacle, the so-called foundation. The process is static and the contact is bilateral, i.e., there is no loss of contact. The friction is modeled with a nonmotonone law. The purpose of this work is to provide an error estimate for the Galerkin method as well as to present and compare two numerical methods for solving the resulting nonsmooth and nonconvex frictional contact problem. The first approach...

Numerical analysis of history-dependent quasivariational inequalities with applications in contact mechanics

Kamran KazmiMikael BarboteuWeimin HanMircea Sofonea — 2014

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

A new class of history-dependent quasivariational inequalities was recently studied in [M. Sofonea and A. Matei, History-dependent quasivariational inequalities arising in contact mechanics. 22 (2011) 471–491]. Existence, uniqueness and regularity results were proved and used in the study of several mathematical models which describe the contact between a deformable body and an obstacle. The aim of this paper is to provide numerical analysis of the quasivariational inequalities introduced in the...

Numerical analysis of a frictionless viscoelastic piezoelectric contact problem

Mikael BarboteuJose Ramon FernándezYoussef Ouafik — 2008

ESAIM: Mathematical Modelling and Numerical Analysis

In this work, we consider the quasistatic frictionless contact problem between a viscoelastic piezoelectric body and a deformable obstacle. The linear electro-viscoelastic constitutive law is employed to model the piezoelectric material and the normal compliance condition is used to model the contact. The variational formulation is derived in a form of a coupled system for the displacement and electric potential fields. An existence and uniqueness result is recalled. Then, a fully discrete scheme...

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