Variational and numerical analysis of a dynamic elasto-viscoplastic piezoelectric frictional contact problem

Abstract This work studies a mathematical model involving a dynamic contact between two elasto-viscoplastic piezoelectric bodies with damage. The contact is modeled on a combination of a normal compliance and a normal damped response law associated with friction. We derive a variational formulation of the problem and we prove the existence and uniqueness result of the weak solution. The proof is based on the classical existence and uniqueness result for parabolic inequalities, differential equations and fixed-point arguments. This paper examines a friction problem between two piezoelectric bodies that are elastic- viscoplastic. The study uses both numerical and analytical methods. The contact surface is assumed to have a thin layer of lubricant, and a damped response contact condition is considered. The problem also takes into account electrical and frictional effects. The paper proves the existence of a unique weak solution to the problem by using variational inequalities and a fixed point argument. Additionally, a fully discrete approximation is investigated using the Euler scheme and finite element method for the spatial variable and time derivatives. Error estimates are then calculated, leading to convergence results under certain regularity conditions.

• elasto-viscoplasticity
• piezoelectric materials
• frictional contact
• dynamic contact problems
• damages
• normal compliance
• weak solution existence and uniqueness
• variational inequalities
• fixed point argument
• parabolic inequalities
• lubricant layer
• Euler scheme
• error estimates
• finite element analysis

• Contact Mechanics and Variational Inequalities
• Adhesion, Friction, and Surface Interactions
• Advanced Numerical Methods in Computational Mathematics
• elasto-viscoplasticity
• piezoelectric materials
• frictional contact
• dynamic contact problems
• damages
• normal compliance
• weak solution existence and uniqueness
• variational inequalities
• Computational Theory and Mathematics
• Mechanics of Materials
• Computational Mechanics
• Computer Science
• Engineering