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A quasistatic contact problem for viscoelastic materials with friction and damage

Authors
Journal
Nonlinear Analysis Theory Methods & Applications
0362-546X
Publisher
Elsevier
Publication Date
Volume
73
Issue
7
Identifiers
DOI: 10.1016/j.na.2010.05.051
Keywords
  • Hemivariational Inequality
  • Viscoelastic
  • Frictional Contact
  • Damage
  • Stationary Inclusion
  • Weak Solution
Disciplines
  • Mathematics

Abstract

Abstract We consider a mathematical model which describes the frictional contact between a deformable body and a foundation. The process is quasistatic, the material is assumed to be viscoelastic with long memory and the frictional contact is modelled with subdifferential boundary conditions. The mechanical damage of the material is described by the damage function, which is modelled by a nonlinear partial differential equation. We derive the variational formulation of the problem, which is a coupled system of a hemivariational inequality and a parabolic equation. Then we prove the existence of a unique weak solution to the model. The proof is based on arguments of abstract stationary inclusion and a fixed point theorem.

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