A piezoelectric contact problem with normal compliance

Volume 32 / 2005

Mircea Sofonea, Youssef Ouafik Applicationes Mathematicae 32 (2005), 425-442 MSC: 74M10, 74M15, 49J40, 74M99. DOI: 10.4064/am32-4-5

Abstract

We consider a mathematical model which describes the static frictional contact between a piezoelectric body and an insulator foundation. We use a nonlinear electroelastic constitutive law to model the piezoelectric material and the normal compliance condition associated to a version of Coulomb's friction law to model the contact. We derive a variational formulation for the model which is in the form of a coupled system involving the displacement and the electric potential fields. Then we provide the existence of a weak solution to the problem and, under a smallness assumption, its uniqueness. We also study the dependence of the solution on the contact conditions and derive a convergence result.

Authors

  • Mircea SofoneaLaboratoire de Mathématiques et Physique pour les Systèmes
    Université de Perpignan
    52 Avenue de Paul Alduy
    66860 Perpignan, France
    e-mail
  • Youssef OuafikLaboratoire de Mathématiques et Physique pour les Systèmes
    Université de Perpignan
    52 Avenue de Paul Alduy
    66 860 Perpignan, France
    e-mail

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