Journal of Applied Mathematics

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

J. R. Fernández and M. Sofonea

Full-text: Open access

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.

Article information

Source
J. Appl. Math., Volume 2003, Number 2 (2003), 87-114.

Dates
First available in Project Euclid: 7 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.jam/1049725710

Digital Object Identifier
doi:10.1155/S1110757X03202023

Mathematical Reviews number (MathSciNet)
MR1980386

Zentralblatt MATH identifier
1064.74134

Subjects
Primary: 74M15: Contact 74S05
Secondary: 74C10 74R20

Citation

Fernández, J. R.; Sofonea, M. Variational and numerical analysis of the Signorini′s contact problem in viscoplasticity with damage. J. Appl. Math. 2003 (2003), no. 2, 87--114. doi:10.1155/S1110757X03202023. https://projecteuclid.org/euclid.jam/1049725710


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