An Eulerian multi-material scheme for elastic–plastic impact and penetration problems involving large material deformations

Abstract

An Eulerian multi-material scheme is developed for studying elastic–plastic impact and penetration problems involving large material deformations and shock waves. It consists of a Lagrangian plus remap (onto the original mesh) strategy at each time-step. The stress components of each material in a mixed cell are computed independently by assuming a common strain-rate to all materials. Similarly, the energy of each material in a mixed cell is updated independently and the mean pressure is determined using volume weighted average. This simplified approach eliminates commonly used iteration based pressure relaxation procedures and equation of state (EOS) closure models to find an equilibrium pressure in a mixed cell. A similar procedure is used to find equivalent stress in a mixed cell. The volume fraction of each material in a mixed cell is updated using a volume-of-fluid (VOF) interface tracking scheme. A new predictor–corrector (PC) scheme is developed to integrate the governing equations of the proposed multi-material model. The remapping of the stress components of the individual materials is achieved by a combination of a second-order monotonic upwind scheme and the VOF method. It is demonstrated that, despite using a ‘simple’ volume weighted scheme for calculating the total mean stress in mixed cells, the proposed scheme yields reasonable agreement with known analytical and experimental results of various impact and penetration problems.