An extended finite element formulation for contact in multi-material arbitrary Lagrangian-Eulerian calculations

A contact method for the multi-dimensional Lagrangian step in multi-material arbitrary Lagrangian-Eulerian (ALE) formulations is presented. The extended finite element method (X-FEM) is used to create independent fields (i.e. velocity, strain rate, force, mass, etc.) for each material in the problem. The accelerations of the multi- material nodes are obtained by coupling the material force and mass fields as a function of the prescribed contact; similarly, the velocities of the multi-material nodes are recalculated using the conservation of momentum when the prescribed contact requires it. The coupling procedures impose the same nodal velocity on the coupled materials in the direction normal to their interface during the time step update. As a result, the overlap of materials is prevented and unwanted separation does not occur. Three different contacts are treated: perfectly bonded, frictionless slip, and slip with friction. Example impact problems are solved and the numerical solutions are presente