Summary.
In this paper we consider a frictionless contact problem between an elastic–viscoplastic body and an obstacle. The process is assumed to be quasistatic and the contact is modeled with normal compliance. We present a variational formulation of the problem and prove the existence and uniqueness of the weak solution, using strongly monotone operators arguments and Banach's fixed point theorem. We also study the numerical approach to the problem using spatially semi-discrete and fully discrete finite elements schemes with implicit and explicit discretization in time. We show the existence of the unique solution for each of the schemes and derive error estimates on the approximate solutions. Finally, we present some numerical results involving examples in one, two and three dimensions.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received May 20, 2000 / Revised version received January 8, 2001 / Published online June 7, 2001
Rights and permissions
About this article
Cite this article
Fernández-García, J., Sofonea, M. & no, J. A frictionless contact problem for elastic–viscoplastic materials with normal compliance: Numerical analysis and computational experiments. Numer. Math. 90, 689–719 (2002). https://doi.org/10.1007/s002110100306
Issue Date:
DOI: https://doi.org/10.1007/s002110100306