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A quasistatic contact problem with slip-dependent coefficient of friction

✍ Scribed by Amina Amassad; Meir Shillor; Mircea Sofonea

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 146 KB
Volume: 22
Category: Article
ISSN: 0170-4214
DOI: 10.1002/(sici)1099-1476(199902)22:3<267::aid-mma40>3.0.co;2-a

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✦ Synopsis

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.

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