Dual methods for frictional contact problem with electroelastic-locking materials

Abstract

We consider an electroelastic-locking material coming in frictional contact with a conductive foundation. The locking character makes the solution belongs to convex set and the contact is modelled with Coulomb friction which leads to more constraints. Existence and uniqueness of the solution is proved using results obtained in elliptic quasi-variational inequality theory and Banach fixed point theorem. The term coupling the mechanical field and the electric potential in the problem is non symmetric which makes us unable to get constrained minimization problem. To overcome this difficulty, we use a convergent fixed point iterative scheme and alternating directions method of multipliers (ADMM). The solutions are computed basing variational inequalities and both Lagrange (KKT conditions) and Fenchel convex dualities. Two numerical examples are implemented to show solutions and the efficiency of our approach.