A Signorini frictionless contact problem for viscoelastic materials with long-term memory

Á. D. Rodríguez Arós, M. Sofonea and J. M. Viaño
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Á. D. Rodríguez Arós: Universidade de Santiago de Compostela, Departamento de Matemática Aplicada
M. Sofonea: Université de Perpignan, Laboratoire de Théorie des Systèmes
J. M. Viaño: Universidade de Santiago de Compostela, Departamento de Matemática Aplicada

A chapter in Numerical Mathematics and Advanced Applications, 2003, pp 327-336 from Springer

Abstract: Summary We consider a quasistatic problem which models the contact between a deformable body and an obstacle, the so-called foundation. The material is assumed to have a viscoelastic behavior that we model with a constitutive law with long-term memory; thus, at each moment of time, the stress tensor depends not only on the present strain tensor, but also on its whole history. The contact is frictionless and is modeled by the well-known Signorini conditions. We derive a weak formulation of the problem and, under appropriate regularity hypotheses, we prove its unique solvability. We also discuss a fully discrete scheme for which we obtain error estimates and convergence results. Finally, in order to verify the accuracy of the numerical method, we present numerical simulations for a one-dimensional test problem.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-88-470-2089-4_30

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DOI: 10.1007/978-88-470-2089-4_30

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