A mixture theory for contact in multi-material Eulerian formulations

Multi-material Eulerian methods are attractive for solving a broad range of highly nonlinear problems in solid mechanics because they per mit arbitrarily large deformations and automatically allow new free surfaces to evolve. Many of these problems involve the contact and separation of surfaces. There is an extensive literature for including contact inequality constraints in Lagrangian finite element methods, but little consideration has been given to contact in Eulerian methods. The contact forces bt tween adjacent bodies are governed by the mixture theory in the Eulerian formulation, making the mixture theory the natural starting point in the treatment of the contact inequalities. A mixture theory that equilibrates the traction across the material interface and limits the shear stress according to a Coulomb friction law is developed.