A quasistatic contact problem with slip-dependent coefficient of friction

• Published in: Mathematical methods in the applied sciences Vol. 22; no. 3; pp. 267 - 284
• Main Authors: Amassad, Amina, Shillor, Meir, Sofonea, Mircea
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01-02-1999; Wiley; Teubner
• Subjects: bilateral contact with friction; Coulomb's modified friction law; Exact sciences and technology; fixed point; Fundamental areas of phenomenology (including applications); Mechanical contact (friction...); Physics; slip-dependent coefficient of friction; Solid mechanics; Structural and continuum mechanics; variational inequality; viscoelastic constitutive law; Constitutive equation; Solution uniqueness; Viscoelasticity; Coulomb law; Contact binary; Existence of solution; Weak solution; Lipschitz boundary; Variational inequality; Slip system; Friction coefficient; Slip dependence; Variational techniques; Outer normal
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/(SICI)1099-1476(199902)22:3<267::AID-MMA40>3.0.CO;2-A

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.