A mixed variational formulation for a piezoelectric frictional contact problem

作者：Matei Andaluzia; Sofonea Mircea^*

来源：IMA Journal of Applied Mathematics, 2017, 82(2): 334-354.

DOI：10.1093/imamat/hxw052

• piezoelectric material
• frictional contact
• conductive foundation
• evolutionary mixed variational formulation
• Lagrange multiplier
• weak solution

We consider a mathematical model which describes the quasistatic contact of a piezoelectric body with an electrically conductive foundation. The material's behaviour is described by means of an electroviscoelastic constitutive law, the contact is bilateral and is associated to Tresca's law of dry friction. We derive a mixed variational formulation of the problem, which is in form of an evolutionary system for the displacement field, the electric potential and two Lagrange multipliers. Then we provide the existence of a unique weak solution to the model. Also, under additional assumptions, we establish its continuous dependence with respect to the friction bound and the electric conductivity coefficient.

• 出版日期2017-4