On the frictionless unilateral contact of two viscoelastic bodies

Autor: M. Barboteu, T.-V. Hoarau-Mantel, M. Sofonea
Jazyk: angličtina
Rok vydání: 2003
Předmět:
Zdroj: Journal of Applied Mathematics, Vol 2003, Iss 11, Pp 575-603 (2003)
Druh dokumentu: article
ISSN: 1110-757X
1687-0042
1110757X
DOI: 10.1155/S1110757X03212043
Popis: 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.
Databáze: Directory of Open Access Journals
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