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

Multi-material Eulerian and arbitrary Lagrangian–Eulerian methods were originally developed for solving hypervelocity impact problems, but they are attractive for solving a broad range of problems having large deformations, the evolution of new free surfaces, and chemical reactions. The contact, separation, and slip between two surfaces have traditionally been addressed by the mixture theory, however the accuracy of this approach is severely limited. To improve the accuracy, an extended finite element formulation is developed and example calculations are presented. As a side benefit, the mixture theory is eliminated from the multi-material formulation, eliminating the issues associated with the equilibration time between adjacent materials. By design, the new formulation is relatively simple to implement in existing multi-material codes, parallelizes without difficulty, and has a low memory burden. Copyright 2006 John Wiley & Sons, Ltd