A finite volume penalty-based implicit procedure for the treatment of the frictionless contact boundaries

This article presents a new implicit coupling procedure for mechanical contact simulations using an implicit cell-centred finite volume method. Both contact boundaries are treated as Neumann conditions, where the prescribed contact force is calculated using a penalty law, which is linearised and updated within the iterative solution procedure. Compared to the currently available explicit treatment, the implicit treatment offers better efficiency for the same accuracy. This is achieved with the proposed implicit linearisation, which replaces the explicit under-relaxation of the contact force. The proposed procedure, intended for frictionless contact of Hookean solids, can handle non-conformal contact interface discretisations and faces in partial contact. The accuracy and efficiency of the implicit approach are compared with the explicit procedure on four benchmark problems, where it is shown that the proposed method can significantly improve efficiency and robustness.