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Zbl 1142.74031
Campo, M.; Fernández, J.R.; Rodr{\'\i}guez-Arós, Á.
A quasistatic contact problem with normal compliance and damage involving viscoelastic materials with long memory. (English)
[J] Appl. Numer. Math. 58, No. 9, 1274-1290 (2008). ISSN 0168-9274

Summary: We study a model for quasistatic frictionless contact between a viscoelastic body with long memory and a foundation. The material constitutive relation is assumed to be nonlinear, and the contact is modelled with the normal compliance condition, i.e., the obstacle is assumed deformable. The mechanical damage of the material, caused by excessive stress or strain, is described by the damage function, which is modelled by a nonlinear partial differential equation. We derive a variational formulation for the problem and prove the existence of its unique weak solution. Then, we introduce a fully discrete scheme for the numerical solutions of the problem, based on the finite element method to approximate the spatial variable and on Euler scheme to discretize the time derivatives, and we obtain error estimates for approximate solutions. Finally, some numerical results are presented for two-dimensional test problems.

MSC 2000:: *74M15 Contact
74D05 Linear constitutive equations
74H20 Existence of solutions
74H25 Uniqueness of solutions
74S05 Finite element methods
74S20 Finite difference methods

Keywords: finite elements; error estimates; existence; Euler scheme

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