Analysis of a piezoelectric contact problem with subdifferential boundary condition

Stanisław Migórski (1) , Anna Ochal (1) , Mircea Sofonea (2)

1 Institute of Computer Science [Krakow]
2 LAMPS - LAboratoire de Modélisation Pluridisciplinaire et Simulations

We consider a mathematical model which describes the frictionless contact between a piezoelectric body and a foundation. The contact process is quasi-static and the foundation is assumed to be insulated. The novelty of the model consists in the fact that the material behaviour is described with an electro-elastic–visco-plastic constitutive law and the contact is modelled with a subdifferential boundary condition. We derive a variational formulation of the problem which is in the form of a system coupling two nonlinear integral equations with a history-dependent hemivariational inequality and a time-dependent linear equation. We prove the existence of a weak solution to the problem and, under additional assumptions, its uniqueness. The proof is based on a recent result on history-dependent hemivariational inequalities obtained by Migórski, Ochal and Sofonea in 2011.

Domaines: Mathématiques [math]

Stanisław Migórski, Anna Ochal, Mircea Sofonea. Analysis of a piezoelectric contact problem with subdifferential boundary condition. Proceedings of the Royal Society of Edinburgh: Section A, Mathematics, 2014, 144 (05), pp.1007-1025. ⟨10.1017/S0308210513000607⟩. ⟨hal-01142125⟩