A dynamic frictional contact problem for piezoelectric materials
This important paper deals with a mathematical model which describes the frictional contact between a piezoelectric body and an electrically conductive foundation. The piezoelectric materials, with a strong coupling between the mechanical stress and the electric potential, are extensively used as sensors and switches in engineering applications, and are mostly involved in contact. Here, in order to develop the above model, the authors use some assumptions on the data and derive the variational formulation of the problem, which is in the form of a system coupling a second-order hemivariational inequality for the displacement field with a time-dependent hemivariational inequality for the electric potential. The main result: the new mathematical model describes the frictional contact between an electro-viscoelastic body and a conductive foundation. The novelty of the proposed model consists in the fact that the process is dynamic, the material behavior is described by an electro-viscoelastic constitutive law, and both the frictional contact and electrical condition on the contact surface are modeled with subdifferential boundary conditions involving nonconvex functionals. A physical process in which contact, friction and piezoelectric are involved, is described in detail. Further the authors show that the resulting model leads to a well-posed mathematical problem. To this end the authors use the framework of evolutionary hemivariational inequalities. The existence of a unique weak solution to the introduced model is proved. The proof is based on arguments of abstract second-order evolutionary inclusions.
scientific article; zbMATH DE number 5625395