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Quasistatic problems in contact mechanics

Meir Shillor — 2001

International Journal of Applied Mathematics and Computer Science

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...

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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