An Algorithm for Eulerian Front Tracking for Solid Deformation

An attractive approach for simulation of large deformation solid dynamics is to combine Eulerian nite diierencing with material interface tracking. The Eulerian computational mesh is not subject to mesh distortion, and tracking eliminates spurious numerical diiusion at interfaces and the need for mixed-material computational cells. We have developed such an approach within the framework of the front tracking method, as implemented in the FronTier code. Our two-dimensional solid dynamics module is based on a fully conservative formulation of the governing equations for large-strain deformation, a hyperelas-tic equation of state that allows for large volume change, and a rate-dependent plasticity model. It features conservative nite diierencing, use of a Riemann solver to enforce the Rankine-Hugoniot conditions at material interfaces, and an implicit method for integrating the plastic source terms. This paper presents an overview of solid dynamics in FronTier and some preliminary applications to high-velocity expanding ring and shock-accelerated interface problems. 1. Introduction The simulation of large strain, dynamic, multi-material deformation and failure is a dii-cult and important computational challenge. Because such simulations are often performed at the micro-and meso-scale to support development of macro-scale material models, a premium is placed on high resolution numerical methods and physical delity of the underlying constitutive descriptions. An attractive approach for such simulations is to combine an Eulerian nite diierence method with explicit material interface tracking. The xed Eulerian computational mesh is not subject to mesh distortion and explicit tracking of interfaces eliminates spurious numerical diiusion and the need for problematic mixed-material computational cell models. Most importantly, explicit tracking aaords the opportunity to apply special algorithms at the interfaces which are particularly important features in the ow eld.