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Analysis and numerical approximation of an elastic frictional contact problem with normal compliance

Weimin HanMircea Sofonea — 1999

Applicationes Mathematicae

We consider the problem of frictional contact between an elastic body and an obstacle. The elastic constitutive law is assumed to be nonlinear. The contact is modeled with normal compliance and the associated version of Coulomb's law of dry friction. We present two alternative yet equivalent weak formulations of the problem, and establish existence and uniqueness results for both formulations using arguments of elliptic variational inequalities and fixed point theory. Moreover, we show the continuous...

A piezoelectric contact problem with normal compliance

Mircea SofoneaYoussef Ouafik — 2005

Applicationes Mathematicae

We consider a mathematical model which describes the static frictional contact between a piezoelectric body and an insulator foundation. We use a nonlinear electroelastic constitutive law to model the piezoelectric material and the normal compliance condition associated to a version of Coulomb's friction law to model the contact. We derive a variational formulation for the model which is in the form of a coupled system involving the displacement and the electric potential fields. Then we provide...

A convergence result for evolutionary variational inequalities and applications to antiplane frictional contact problems

Mircea SofoneaMohamed Ait Mansour — 2004

Applicationes Mathematicae

We consider a class of evolutionary variational inequalities depending on a parameter, the so-called viscosity. We recall existence and uniqueness results, both in the viscous and inviscid case. Then we prove that the solution of the inequality involving viscosity converges to the solution of the corresponding inviscid problem as the viscosity converges to zero. Finally, we apply these abstract results in the study of two antiplane quasistatic frictional contact problems with viscoelastic and elastic...

Quasistatic frictional problems for elastic and viscoelastic materials

Oanh ChauDumitru MotreanuMircea Sofonea — 2002

Applications of Mathematics

We consider two quasistatic problems which describe the frictional contact between a deformable body and an obstacle, the so-called foundation. In the first problem the body is assumed to have a viscoelastic behavior, while in the other it is assumed to be elastic. The frictional contact is modeled by a general velocity dependent dissipation functional. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of evolution variational...

Tykhonov well-posedness of a heat transfer problem with unilateral constraints

Mircea SofoneaDomingo A. Tarzia — 2022

Applications of Mathematics

We consider an elliptic boundary value problem with unilateral constraints and subdifferential boundary conditions. The problem describes the heat transfer in a domain D d and its weak formulation is in the form of a hemivariational inequality for the temperature field, denoted by 𝒫 . We associate to Problem 𝒫 an optimal control problem, denoted by 𝒬 . Then, using appropriate Tykhonov triples, governed by a nonlinear operator G and a convex K ˜ , we provide results concerning the well-posedness of problems...

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 and simulations of quasistatic frictionless contact problems

José Fernández GarcíaWeimin HanMeir ShillorMircea Sofonea — 2001

International Journal of Applied Mathematics and Computer Science

A summary of recent results concerning the modelling as well as the variational and numerical analysis of frictionless contact problems for viscoplastic materials are presented. The contact is modelled with the Signorini or normal compliance conditions. Error estimates for the fully discrete numerical scheme are described, and numerical simulations based on these schemes are reported.

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