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A quasistatic contact problem with unilateral constraint and slip-dependent friction

Arezki Touzaline (2015)

Applicationes Mathematicae

We consider a mathematical model of a quasistatic contact between an elastic body and an obstacle. The contact is modelled with unilateral constraint and normal compliance, associated to a version of Coulomb's law of dry friction where the coefficient of friction depends on the slip displacement. We present a weak formulation of the problem and establish an existence result. The proofs employ a time-discretization method, compactness and lower semicontinuity arguments.

Hybrid level set phase field method for topology optimization of contact problems

Andrzej Myśliński, Konrad Koniarski (2015)

Mathematica Bohemica

The paper deals with the analysis and the numerical solution of the topology optimization of system governed by variational inequalities using the combined level set and phase field rather than the standard level set approach. The standard level set method allows to evolve a given sharp interface but is not able to generate holes unless the topological derivative is used. The phase field method indicates the position of the interface in a blurry way but is flexible in the holes generation. In the...

Subdifferential inclusions and quasi-static hemivariational inequalities for frictional viscoelastic contact problems

Stanisław Migórski (2012)

Open Mathematics

We survey recent results on the mathematical modeling of nonconvex and nonsmooth contact problems arising in mechanics and engineering. The approach to such problems is based on the notions of an operator subdifferential inclusion and a hemivariational inequality, and focuses on three aspects. First we report on results on the existence and uniqueness of solutions to subdifferential inclusions. Then we discuss two classes of quasi-static hemivariational ineqaulities, and finally, we present ideas...

Topology optimization of systems governed by variational inequalities

Andrzej Myśliński (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

This paper deals with the formulation of the necessary optimality condition for a topology optimization problem of an elastic body in unilateral contact with a rigid foundation. In the contact problem of Tresca, a given friction is governed by an elliptic variational inequality of the second order. The optimization problem consists in finding such topology of the domain occupied by the body that the normal contact stress along the contact boundary of the body is minimized. The topological derivative...

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