Non-physical finite element modelling of high speed normal crushing of cellular materials

• A novel finite element method for modelling shocks in cellular materials.
• The establishment of non-physical duplicate fields to mirror physical counter parts pertinent to cellular materials.
• The establishment of transport equations for non-physical fields.
• The exact representation of shocks within a classical finite element framework.
• The testing and application of the non-physical approach to cellular impact physics.

This work presents a new FE based methodology for numerical simulation of shock like behaviour in high speed crushing of metallic cellular materials. This recently developed numerical technique is called the non-physical finite element method. The approach is based on integral transport forms of the governing conservation laws and the concept of non-physical variable. With the non-physical variable concept each conservation law gives rise to a non-physical field. Unfortunately this results in a doubling of the number of transport equations and the number of field variables. However, non-physical variables can be shown to possess limiting continuity at any discontinuity in the physical fields. Another feature of the formulation is the presence of a non-physical source term at a discontinuity whose strength is related to the magnitude of the discontinuity in the physical field. One benefit of the approach is the precise annihilation of discontinuous behaviour from the governing finite element equations. Hence, classical continuous finite element approximations can be used with high accuracy to solve the resulting system of equations. The methodology is demonstrated through application to three different models of 1-D in-plane high-velocity impact crushing of a cellular Taylor bar, where numerical results are found to be in excellent correspondence to predictions from analytical models. The present work belongs to the category of finite element based shock capturing techniques.