A method for solving an electro-viscoelastic contact problem with damped response and friction

This paper explores the numerical modeling of quasistatic contact between a visco-electroelastic body and an electrically conductive foundation. The contact behavior is characterized by damped normal response and a local friction law. A variational formulation of the model is developed, and the existence of a unique weak solution is demonstrated, contingent upon a condition of low conductivity for the foundation. We introduce a fully discrete finite element scheme to address the variational problem and provide error estimates for the resulting approximate solution. Additionally, we propose and investigate a successive iterative (decomposition) method, solving two sub-problems for the displacement field and electric potential sequentially at each time step \(t_{n}\) $t_n$ . Convergence of the iterative decomposition method is proven. Lastly, we present numerical results from a two-dimensional test problem to demonstrate the effectiveness of the proposed algorithm.