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An elastic contact problem with adhesion and normal compliance

Sofonea M., Matei A.

Journal of Applied Analysis

2006

Vol. 12, nr 1

19-36

We study a mathematical problem describing the friction- less adhesive contact between an elastic body and a foundation. The adhesion process is modelled by a surface variable, the bonding field, and the contact is modelled with a normal compliance condition; the tangential shear due to the bonding field is included; the elastic consti- tutive law is assumed to be nonlinear and the process is quasistatic. The problem is formulated as a nonlinear system in which the unknowns are the displacement, the stress and the bonding field. The existence of a unique weak solution for the problem is established by using arguments for differential equations followed by the construction of an appropriate contraction mapping.

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.