Journal of Applied Mathematics

Journal of Applied Mathematics / 2003 / Article

Open Access

Volume 2003 |Article ID 246790 | https://doi.org/10.1155/S1110757X03212043

M. Barboteu, T.-V. Hoarau-Mantel, M. Sofonea, "On the frictionless unilateral contact of two viscoelastic bodies", Journal of Applied Mathematics, vol. 2003, Article ID 246790, 29 pages, 2003. https://doi.org/10.1155/S1110757X03212043

On the frictionless unilateral contact of two viscoelastic bodies

Received12 Dec 2002
Revised10 Jun 2003

Abstract

We consider a mathematical model which describes the quasistatic contact between two deformable bodies. The bodies are assumed to have a viscoelastic behavior that we model with Kelvin-Voigt constitutive law. The contact is frictionless and is modeled with the classical Signorini condition with zero-gap function. We derive a variational formulation of the problem and prove the existence of a unique weak solution to the model by using arguments of evolution equations with maximal monotone operators. We also prove that the solution converges to the solution of the corresponding elastic problem, as the viscosity tensors converge to zero. We then consider a fully discrete approximation of the problem, based on the augmented Lagrangian approach, and present numerical results of two-dimensional test problems.

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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