The Shifted Boundary Method for contact problems

Abstract

We propose an embedded algorithm for contact mechanics based on the Shifted Boundary Method. The contact conditions are applied on a surrogate contact surface in proximity of the true contact surface and Taylor expansions are used to change (shift) both their value and location. This approach is robust, accurate, and avoids integrating the variational formulation on cut cells and related numerical instabilities. Computational experiments in both two and three dimensions are provided to demonstrate the performance of our methodology. The proposed approach offers an advantage whenever bodies of very complex shape come into contact, especially when the shapes are not represented using standard Computer Aided Design (CAD) formats. In all these situations, body-fitted grid generation may become extremely time consuming or completely unfeasible.