Frictional contact problems for electro-viscoelastic materials with long-term memory, damage, and adhesion

Abstract

We consider a quasistatic contact problem between two electro-viscoelastic bodies with long-term memory and damage. The contact is frictional and is modelled with a version of normal compliance condition and the associated Coulomb's law of friction in which the adhesion of contact surfaces is taken into account. We derive a variational formulation for the model and prove an existence and uniqueness result of the weak solution. The proof is based on arguments of evolutionary variational inequalities, a classical existence and uniqueness result on parabolic inequalities, and Banach fixed point theorem.

Keywords

• Electro-viscoelastic material with long-term memory
• damage
• adhesion
• friction contact
• normal compliance
• variational inequality
• fixed point