Practical methods for the implementation of material strength into an Eulerian hydrocode

Abstract

This study presents the framework and implementation of a material strength model within a two-step Eulerian solution scheme in the MHD hydrocode, B2. The techniques presented in this work provide practical solutions to problems encountered when modelling high strain-rate behaviour of solids in an Eulerian framework. Several novel methods developed in this work resulted in the accurate reproduction of a Taylor anvil-on-rod test in B2 without a complex and computationally expensive interface reconstruction technique. These methods include a complete algorithmic definition of the different components of the stress tensor, ensuring realistic behaviour in low-density mixed cells at the rod-vacuum boundary through a density dependent modification of the yield, implementing automatically generated slip conditions at part boundaries, and damping oscillating numerical instabilities induced by the inclusion of strength. The Taylor test served as a rigorous verification case for the strength model, demonstrating the efficacy of these novel methods. A cross-code comparison against the results of a Lagrangian simulation in Ansys AUTODYN, a well-benchmarked commercial code which employs Young’s Reconstruction, of the Taylor rod deformation revealed a close match with the rod profile predicted by B2. In this article, emphasis is placed on the practical details of the routines required to implement these corrections to facilitate the adoption of three-dimensional material strength models in other Eulerian hydrocodes.