Numerical analysis of a frictionless contact problem for elastic–viscoplastic materials

• Published in: Computer methods in applied mechanics and engineering 2000-10, Vol.190 (1), p.179-191
• Main Authors: Han, Weimin, Sofonea, Mircea
• Format: Article
• Language: English
• Subjects: Computational techniques; Convergence; Cross-disciplinary physics: materials science; rheology; Deformation, plasticity, and creep; Elastic–viscoplastic material; Error estimate; Exact sciences and technology; Finite element method; Finite-element and galerkin methods; Fully discrete approximation; Materials science; Mathematical methods in physics; Physics; Quasistatic frictionless contact problem; Semi-discrete approximation; Time-dependent variational ineqaulity; Treatment of materials and its effects on microstructure and properties
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/S0045-7825(99)00420-X

We consider a mathematical model which describes the unilateral quasistatic contact of two elastic–viscoplastic bodies. The contact is without friction and it is modeled by the classical Signorini boundary conditions. The model consists of an evolution equation coupled with a time-dependent variational inequality. It has been shown that the variational problem of the model has a unique solution. Here we consider numerical approximations of the problem. We use the finite element method to discretize the spatial domain. Spatially semi-discrete and fully discrete schemes are studied. For both schemes, we show the existence of a unique solution, and derive error estimates. Under appropriate regularity assumptions of the solution, we have the optimal order convergence.