Title: Mathematical modelling of piezoelectric elastic materials

Authors: Allaoua Boudjedour; Mohamed Dalah

Addresses: Department of Mathematics, Faculty of Exact Sciences, Frères Mentouri Constantine University, B.P. 325 Route Ain El Bey, Constantine 25017, Algeria ' Department of Mathematics, Faculty of Exact Sciences, Frères Mentouri Constantine University, B.P. 325 Route Ain El Bey, Constantine 25017, Algeria

Abstract: We consider a quasistatic contact modelled with the regularised friction law for electro-elastic and the foundation is assumed to be electrically conductive. This regularisation is obtained by replacing the function j(.) by the function j_ρ(.), where ρ is a strictly positive parameter. The classical formulation for the antiplane problem is formulated as a time dependent of corresponding variational formulation and is solved by the Banach fixed-point theorem and classical results for variational inequalities. We provide a weak formulation of the contact problem in the form variational system in which the unknowns are the displacement and the stress fields, then we establish the existence of a unique weak solution to the model. Finally, we have given a convergence criterion of the solution as the parameter of regularisation ρ converges to zero.

Keywords: quasistatic contact; electro-elastic material; antiplane; regularised friction law; weak solution; variational formulation.

DOI: 10.1504/IJMMNO.2020.108616

International Journal of Mathematical Modelling and Numerical Optimisation, 2020 Vol.10 No.3, pp.270 - 286

Received: 02 Jul 2019
Accepted: 29 Sep 2019
Published online: 21 Jul 2020 *

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