A variationally consistent contact formulation based on a mixed interpolation point method and isogeometric discretization

Abstract

This work enhances the robustness of the standard displacement-based (penalty Gauss-point-to-segment) contact formulation by applying the so-called Mixed Interpolation Point method (MIP). We consider a smooth isogeometric discretization of the contact surface in order to avoid various artificial discontinuities of the normal contact gap function. Like any existing MIP-enhanced formulation in terms of implementation, the proposed MIP contact formulation only requires a minor modification from an existing implementation of the standard contact formulation. Nevertheless, the improvement in robustness is shown to be quite significant, which often enables the simulation of contact problems with a larger load step size for efficiency and/or a larger penalty parameter for accuracy in the contact constraint. The formalism of the proposed MIP contact method is based on the idea of relaxing the contact constitution at integration points. To this end, at first the contact pressure is considered as an additional unknown apart from the displacement field, and the perturbed Lagrange multiplier potential is used to enforce the contact constraint. The MIP method then eliminates the contact pressure unknown directly at integration points, instead of discretizing it as it is done in the standard mixed contact formulations. As a result, the residual vector is identical to the standard displacement-based contact formulation. However, the resulting tangent stiffness matrix is different, as the MIP tangent is now based on an extrapolation of the contact pressure iteratively over Newton iterations. Several challenging numerical examples are presented to illustrate the accuracy, robustness and efficiency of the proposed formulation.