Journal of Applied Mathematics
Volume 2003 (2003), Issue 11, Pages 575-603

On the frictionless unilateral contact of two viscoelastic bodies

M. Barboteu, T.-V. Hoarau-Mantel, and M. Sofonea

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.


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.