Journal of Applied Mathematics

Journal of Applied Mathematics / 2003 / Article

Open Access

Volume 2003 |Article ID 409319 | https://doi.org/10.1155/S1110757X03202023

J. R. Fernández, M. Sofonea, "Variational and numerical analysis of the Signorini′s contact problem in viscoplasticity with damage", Journal of Applied Mathematics, vol. 2003, Article ID 409319, 28 pages, 2003. https://doi.org/10.1155/S1110757X03202023

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

Received11 Feb 2002

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.

Copyright © 2003 Hindawi Publishing Corporation. 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.


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