Dual formulation of a viscoplasticcontact problem with unilateral constraint

Andaluzia Matei; Mircea Sofonea

doi:10.3934/dcdss.2013.6.1587

Article Contents

2013, Volume 6, Issue 6: 1587-1598. Doi: 10.3934/dcdss.2013.6.1587

This issue Previous Article Modeling a hard, thin curvilinear interface Next Article Prolegomena to studies on dynamic materials and their space-time homogenization

Dual formulation of a viscoplastic contact problem with unilateral constraint

Andaluzia Matei^1, and
Mircea Sofonea^2,

1.
Departement of Mathematics, University of Craiov, A.I. Cuza Street 13, 200585, Craiova
2.
Laboratoire de Mathématiques et Physique pour les Systèmes, Université de Perpignan, 52 Avenue Paul Alduy, 66860 Perpignan

Received: June 2012

Revised: September 2012

Published: December 2013

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Abstract

We consider a mathematical model which describes the contact between a viscoplastic body and an obstacle, the so-called foundation. The process is quasistatic, the contact is frictionless and is modelled with unilateral constraint. We derive a variational formulation of the model which leads to a history-dependent quasivariational inequality for stress field, associated to a time-dependent convex. Then we prove the unique weak solvability of the model. The proof is based on an abstract existence and uniqueness result obtained in [11].

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Mathematics Subject Classification: Primary: 74M15, 74G25; Secondary: 49J40.

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References

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