Analysis and numerical solution of a piezoelectric frictional contact problem |
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Authors: | Mircea Sofonea Kamran Kazmi Mikael Barboteu Weimin Han |
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Affiliation: | 1. Laboratoire de Mathématiques et Physique, University of Perpignan, 52 Avenue Paul Alduy, 66860 Perpignan, France;2. Department of Mathematics, University of Wisconsin Oshkosh, Oshkosh, WI 54901, USA;3. Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA |
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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. |
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Keywords: | Piezoelectric material Electro-elastic&ndash visco-plastic constitutive law Normal compliance Coulomb&rsquo s law Quasivariational inequality Finite element method |
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