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A quasistatic contact problem with slip‐dependent coefficient of friction
Authors:Amina Amassad  Meir Shillor  Mircea Sofonea
Abstract:We consider a mathematical model which describes the bilateral quasistatic contact of a viscoelastic body with a rigid obstacle. The contact is modelled with a modified version of Coulomb's law of dry friction and, moreover, the coefficient of friction is assumed to depend either on the total slip or on the current slip. In the first case, the problem depends upon contact history. We present the classical formulations of the problems, the variational formulations and establish the existence and uniqueness of a weak solution to each of them, when the coefficient of friction is sufficiently small. The proofs are based on classical results for elliptic variational inequalities and fixed point arguments. We also study the dependence of the solutions on the perturbations of the friction coefficient and obtain a uniform convergence result. Copyright © 1999 John Wiley & Sons, Ltd.
Keywords:viscoelastic constitutive law  bilateral contact with friction  Coulomb's modified friction law  slip‐dependent coefficient of friction  variational inequality  fixed point
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