Journal of Applied Mathematics
Volume 2003 (2003), Issue 11, Pages 575-603
doi:10.1155/S1110757X03212043
On the frictionless unilateral contact of two viscoelastic bodies
Laboratoire de Théorie des Systèmes, Université de Perpignan, 52 avenue de Villeneuve, Perpignan 66860, France
Received 12 December 2002; Revised 10 June 2003
Copyright © 2003 M. Barboteu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We consider a mathematical model which describes the quasistatic
contact between two deformable bodies. The bodies are assumed to
have a viscoelastic behavior that we model with Kelvin-Voigt
constitutive law. The contact is frictionless and is modeled with
the classical Signorini condition with zero-gap
function. We derive a variational formulation of the problem and
prove the existence of a unique weak solution to the model by
using arguments of evolution equations with maximal monotone
operators. We also prove that the solution converges to the
solution of the corresponding elastic problem, as the viscosity
tensors converge to zero. We then consider a fully discrete
approximation of the problem, based on the augmented Lagrangian
approach, and present numerical results of two-dimensional test
problems.