A unilateral contact problem with slip-dependent friction
Volume 43 / 2016
Applicationes Mathematicae 43 (2016), 105-116
MSC: 74B20, 74M15, 49J40.
DOI: 10.4064/am2258-11-2015
Published online: 26 November 2015
Abstract
We consider a mathematical model which describes a static contact between a nonlinear elastic body and an obstacle. The contact is modelled with Signorini's conditions, associated with a slip-dependent version of Coulomb's nonlocal friction law. We derive a variational formulation and prove its unique weak solvability. We also study the finite element approximation of the problem and obtain an optimal error estimate under extra regularity for the solution. Finally, we establish the convergence of an iterative method to the finite element problem.