A frictional contact problem for an electro-viscoelastic body




Lerguet, Zhor
Shillor, Meir
Sofonea, Mircea

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Texas State University-San Marcos, Department of Mathematics


A mathematical model which describes the quasistatic frictional contact between a piezoelectric body and a deformable conductive foundation is studied. A nonlinear electro-viscoelastic constitutive law is used to model the piezoelectric material. Contact is described with the normal compliance condition, a version of Coulomb's law of dry friction, and a regularized electrical conductivity condition. A variational formulation of the model, in the form of a coupled system for the displacements and the electric potential, is derived. The existence of a unique weak solution of the model is established under a smallness assumption on the surface conductance. The proof is based on arguments of evolutionary variational inequalities and fixed points of operators.



Piezoelectric, Frictional contact, Normal compliance, Fixed point, Variational inequality


Lerguet, Z., Shillor, M., & Sofonea, M. (2007). A frictional contact problem for an electro-viscoelastic body. <i>Electronic Journal of Differential Equations, 2007</i>(170), pp. 1-16.


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