Applications of Mathematics

, Volume 47, Issue 4, pp 341–360

Quasistatic Frictional Problems for Elastic and Viscoelastic Materials

  • Oanh Chau
  • Dumitru Motreanu
  • Mircea Sofonea
Article

DOI: 10.1023/A:1021753722771

Cite this article as:
Chau, O., Motreanu, D. & Sofonea, M. Applications of Mathematics (2002) 47: 341. doi:10.1023/A:1021753722771

Abstract

We consider two quasistatic problems which describe the frictional contact between a deformable body and an obstacle, the so-called foundation. In the first problem the body is assumed to have a viscoelastic behavior, while in the other it is assumed to be elastic. The frictional contact is modeled by a general velocity dependent dissipation functional. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of evolution variational inequalities and fixed-point arguments. We also prove that the solution of the viscoelastic problem converges to the solution of the corresponding elastic problem, as the viscosity tensor converges to zero. Finally, we describe a number of concrete contact and friction conditions to which our results apply.

elastic materialviscoelastic materialfrictional contactevolution variational inequalityfixed pointweak solutionapproach to elasticitysubdifferential boundary conditions

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2002

Authors and Affiliations

  • Oanh Chau
    • 1
  • Dumitru Motreanu
    • 1
  • Mircea Sofonea
    • 1
  1. 1.Laboratoire de Theorie des SystemesUniversite de PerpignanPerpignanFrance