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Analysis and numerical solution of a piezoelectric frictional contact problem
Journal article   Open access   Peer reviewed

Analysis and numerical solution of a piezoelectric frictional contact problem

Mircea Sofonea, Kamran Kazmi, Mikael Barboteu and Weimin Han
Applied mathematical modelling, Vol.36(9), pp.4483-4501
09/2012
DOI: 10.1016/j.apm.2011.11.077
url
https://doi.org/10.1016/j.apm.2011.11.077View
Published (Version of record) Open Access

Abstract

We consider a mathematical model which describes the frictional contact between an electro-elastic–visco-plastic body and a conductive foundation. The contact is modelled with normal compliance and a version of Coulomb’s law of dry friction, in which the stiffness and the friction coefficients depend on the electric potential. We derive a variational formulation of the problem and we prove an existence and uniqueness result. The proof is based on a recent existence and uniqueness result on history-dependent quasivariational inequalities obtained in [15]. Then we introduce a fully discrete scheme for solving the problem and, under certain solution regularity assumptions, we derive an optimal order error estimate. Finally, we present some numerical results in the study of a two-dimensional test problem which describes the process of contact in a microelectromechanical switch.
Finite element method Piezoelectric material Electro-elastic–visco-plastic constitutive law Quasivariational inequality Normal compliance Coulomb’s law

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