Journal of Applied Mathematics
Volume 2003 (2003), Issue 2, Pages 87-114
doi:10.1155/S1110757X03202023
Variational and numerical analysis of the Signorini′s contact problem in viscoplasticity with damage
1Departamento de Matemática Aplicada, Facultade de Matemáticas, Universidade de Santiago de Compostela, Campus Universitario Sur, Santiago de Compostela 15782, Spain
2Laboratoire de Thétorie des Systètmes, Université de Perpignan, 52 aven ue de Villeneuve, Perpignan Cedex 66860, France
Received 11 February 2002
Copyright © 2003 J. R. Fernández and M. Sofonea. 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.
Abstract
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 and study a fully discrete scheme for the numerical solutions of the problem. An optimal order error
estimate is derived for the approximate solutions under suitable solution regularity. Numerical examples are presented to show the performance of the method.