Analysis and numerical solution of a piezoelectric frictional contact problem

作者：Sofonea Mircea; Kazmi Kamran^*; Barboteu Mikael; Han Weimin

来源：Applied Mathematical Modelling, 2012, 36(9): 4483-4501.

DOI：10.1016/j.apm.2011.11.077

• Piezoelectric material
• Electro-elastic-visco-plastic constitutive law
• Normal compliance
• Coulomb%26apos
• s law
• Quasivariational inequality
• Finite element method

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%26apos;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.

• 出版日期2012-9