Contact in a multi-material Eulerian finite element formulation Original Research Article

In a multi-material Eulerian formulation for problems in solid mechanics, the default interaction between the surfaces of adjacent materials is perfect bonding. In contrast, for the Lagrangian formulation, the surfaces donʹt interact and may pass through each other freely unless a contact algorithm is introduced to enforce the contact inequality constraints. Sophisticated contact algorithms have been developed for Lagrangian calculations, and are routinely used in large deformation applications such as automobile crashworthiness. In comparison, the Eulerian finite element method lags far behind the Lagrangian finite element method in modeling contact. A natural application for the Eulerian formulation is machining, which includes large deformations, material failure, and contact of a tool with a workpiece, making its simulation a challenging problem. The simulation of the isolated chips involving material failure due to shear bands is used as a test problem to investigate the strength and weakness of the different approaches to implementing contact in multi-material Eulerian calculations.