Original scientific paper

https://doi.org/10.3336/gm.51.2.08

Analysis of a Signorini problem with nonlocal friction in thermo-piezoelectricity

H. Benaissa orcid.org/0000-0002-5035-3838 ; Univ Hassan 1, Laboratory MISI, 26000 Settat, Morocco
EL-H. Essoufi orcid.org/0000-0003-1563-2871 ; Univ Hassan 1, Laboratory MISI, 26000 Settat, Morocco
R. Fakhar ; Univ Hassan 1, Laboratory LS3M, 25000 Khouribga, Morocco

Abstract

We consider a mathematical model which describes the frictional unilateral contact between a thermo-piezoelectric body and a rigid electrically conductive foundation. The thermo-piezoelectric constitutive law is assumed to be nonlinear and the contact is modeled with the Signorini condition, the nonlocal Coulomb friction law with slip dependent friction coefficient and the regularized electrical and thermal conductivity conditions. The variational form of this problem is a coupled system which consists of a nonlinear variational inequality for the displacement field and two nonlinear variational equations for the electric potential and the temperature. The existence of a unique weak solution to the problem is proved by using abstract results for elliptic variational inequalities and fixed point arguments.

Keywords

Static frictional contact; thermopiezoelectric material; Signorini conditions; Coulomb's friction; frictional heat generation; variational inequality; variational analysis; fixed point process

Hrčak ID:

170044

URI

https://hrcak.srce.hr/170044

Publication date:

3.12.2016.

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