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The Quarterly Journal of Mechanics and Applied Mathematics 2001 54(4):501-522; doi:10.1093/qjmam/54.4.501
© 2001 by Oxford University Press
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Variational and Numerical Analysis of a Frictionless Contact Problem for Elastic–Viscoplastic Materials with Internal State Variables

J. R. Fernández1, W. Han2, M. Sofonea3 and J. M. Viaño4

( 1 Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, España 2 Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA 3 Laboratoire de Théorie des Systèmes, Université de Perpignan, France 4 Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, España )

We consider a quasistatic frictionless contact problem between a deformable body and a foundation. The material is assumed to have a nonlinear behaviour that we model with a rate-type viscoplastic constitutive law involving internal state variables. The contact is modelled with normal compliance. We present a variational formulation of the problem and prove the existence and uniqueness of the weak solution. We then derive error estimates for a fully discrete scheme to solve the problem. Under appropriate regularity assumptions on the exact solution, we establish optimal-order error estimates. Finally, we present numerical examples which show a very good performance of the fully discrete scheme.


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