Title: An X-FEM Formulation for Contact in Multi-Material Arbitrary Lagrangian-Eulerian Calculations

Speaker: Efrem Vitali, Postdoctoral Researcher, Department of Structural Engineering University of California, San Diego          

Date/Time: Tuesday, June 9, 2009, 9:00 – 10:00 am

Location: Bldg 858EL/L1410 (Sandia NM)

Brief Abstract: Multi-material Eulerian formulations were initially introduced to solve hydrodynamic problems. Their ability to automatically generate new interfaces and solve nonlinear large deformation problems make these formulations very attractive for solving solid mechanics problems. However, the development of multi-material elements and contact algorithms for Eulerian formulations has traditionally been challenging. Little work has been done in this direction and literature is scarce. The main contribution is attributed to Benson who pioneered the field with “contact mixture theories”. Mixture theories have proved to work well with multi-material problems presenting fully bonded contact types; however, the limits of these theories arise when a different contact type is required. The failure to correctly express the behavior of other contact types is attributed to the lack of nodal degrees of freedom; a node with more than one material in its support needs extra degrees of freedom in order to describe the behavior of each material. This talk will focus on a new method of enforcing contacts that employs one set of degrees of freedom for each material present in the nodal support (i.e. displacement, velocity, acceleration, mass, etc. fields are created separately for each material); contact between materials is enforced by coupling their nodal velocities and accelerations according to the prescribed contact type. The effectiveness of the new method is presented in different example calculations. Collision and separation are observed in a bouncing cylinder problem. Frictionless slip, slip with friction, and fully bonded contacts are treated in a sliding block and a Taylor anvil examples. A projectile penetration problem emphasizes the importance of sliding surfaces. Finally, a shock compression of steel powder example shows the robustness of the algorithm.  When the results are compared with the existing mixture theories, the improvement is evident. The applications for this algorithm cover a vast range of solid mechanics problems; however, its true effectiveness is achieved with problems presenting large deformations (e.g. materials processing).

CSRI POC: Tom Voth, (505) 844-6004