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A Model for Adhesive Frictional Contact

Sofonea M., Lerguet Z.

Machine Dynamics Problems

2006

Vol. 30, No. 2

158-168

The aim of this paper is to present a mathematical model which describes the quasistatic process of adhesive frictional contact between a deformable body and an obstacle, the so-called foundation. The material's behavior is assumed to be elastic, with a nonlinear constitutive law; the adhesive contact is modelled with a surface variable, the bonding field, associated to the normal compliance condition and the static version of Coulomb's law of dry friction. We describe the assumptions which lead to the mathematical model of the process and derive a variational formulation of the problem; then, under a smallness assumption on the coefficient of friction, we prove the uniqueness of the solution for the model.

Quasistatic Problems in Contact Mechanics

Shillor M.

International Journal of Applied Mathematics and Computer Science

2001

Vol. 11, no 1

189-204

We describe some of our recent results concerning the modeling and analysis of quasistatic contact problems between a deformable body and a foundation. We concentrate mainly on frictional contact, and in some of the problems thermal effects and the wear of the contacting surfaces are also taken into account. We describe the physical processes involved, the mathematical models, their variational formulation and then present statements of our results. We conclude with a description of some unresolved problems.

Numerical Analysis and Simulations of Quasistatic Frictionless Contact Problems

Fernandez Garcia J. R., Han W., Shillor M., Sofonea M.

International Journal of Applied Mathematics and Computer Science

2001

Vol. 11, no 1

205-222

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.