J‐ADMM for a multi‐contact problem in electro‐elastostatics

Abstract

AbstractIn this work we apply a regularized alternating direction method of multiplier of Jacobi type (J‐ADMM) to a frictional multi‐contact (both unilateral and bilateral) problem between an electro‐elastic material and a rigid non conductive foundations. The frictional contact is modelled by the Coulomb friction law. The resulted problem is non symmetric and non coercive. By dissociating the electric potential from the mechanical field, we obtain a symmetric and coercive problem which can be reformulated as a convex minimization problem. We then apply a J‐ADMM for the numerical approximation to the resulting perturbed elastic problem. The resolution of obtained sub‐problems is based on convex dualities. Numerical experiments are proposed to illustrate the efficiency of the proposed approach.