Variational and numerical analysis of a quasistatic viscoelastic problem with normal compliance, friction and damage

[摘要] We consider a model for quasistatic frictional contact between a viscoelastic body and a foundation. The material constitutive relation is assumed to be nonlinear. The mechanical damage of the material, caused by excessive stress or strain, is described by the damage function, the evolution of which is determined by a parabolic inclusion. The contact is modeled with the normal compliance condition and the associated version of Coulomb's law of dry friction. We derive a variational formulation for the problem and prove the existence of its unique weak solution. We then study a fully discrete scheme for the numerical solutions of the problem and obtain error estimates on the approximate solutions. (C) 2001 Elsevier Science B.V. All rights reserved.

[发布日期] 2001-12-15

[关键词] quasistatic frictional contact;viscoelastic material;normal compliance;Coulomb's friction;mechanical damage;variational inequality;variational analysis;numerical analysis;fully discrete scheme;finite element method