A dynamic frictional contact problem for piezoelectric materials
type: Item
instance of: scholarly article
title: A dynamic frictional contact problem for piezoelectric materials
zbMATH Open document ID: 1192.74278
author: Anna Ochal
author: Mircea Sofonea
author: Stanisław Migórski
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-11-05T00:00:00Z
review text: 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.
reviewed by: Jan Lovíšek
Mathematics Subject Classification ID: 74M15
Mathematics Subject Classification ID: 74F15
Mathematics Subject Classification ID: 74M10
Mathematics Subject Classification ID: 74H20
Mathematics Subject Classification ID: 74H25
zbMATH DE Number: 5625395
zbMATH Keywords: hemivariational inequality
zbMATH Keywords: variational formulation
zbMATH Keywords: unique weak solution
zbMATH Keywords: second-order evolutionary inclusions
MaRDI profile type: Publication
full work available at URL: j.jmaa.2009.09.004
OpenAlex ID: W1973239402
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DOI: 10.1016/J.JMAA.2009.09.004
description: scientific article; zbMATH DE number 5625395