Variational and numerical analysis of the Signorini′s contact problem in viscoplasticity with damage

[摘要] We consider the quasistatic Signorini′s contact problem with damage for elastic-viscoplastic bodies. The mechanical damage of the material, caused by excessive stress or strain, is described by a damage function whose evolution is modeled by an inclusion of parabolic type. We provide a variational formulation for the mechanical problem and sketch a proof of the existence of a unique weak solution of the model. We then introduce andstudy a fully discrete scheme for the numerical solutions of the problem.An optimal order errorestimate is derived for the approximate solutions under suitable solution regularity.Numerical examples are presented to show the performance of the method.

[学科分类] 应用数学