The numerical simulation of the behavior of soft and biological materials under shock, penetrating and fragmenting loading conditions continues to be a challenging problem due to the highly non-linear and strain-rate dependent nature of these materials. Over the course of our work focused on the numerical modeling of penetration into soft materials at high rates of loading, we have identified the importance of shear-dependent failure models that seem to be lacking in commonly used particle methods, which primarily use Eulerian descriptions of failure. These existing damage models update the pressure response of a given cell, but not the deviatoric response of an individual material element.
This effort to examine a shear-dependent failure model builds on previous work that uses a particle-based framework to couple a continuum-based visco-hyperelastic constitutive model with an Eulerian-based failure mechanism. While the elastic portion of this material model showed good agreement with experimental data for high-rate loads, an Eulerian-based failure approach did not accurately capture the complex mechanics of penetration problems in soft materials. This is attributed to how the previous algorithms employ void insertion to deal with failed material, which only relies on pressure terms to determine the extent of failure. Here we extend the algorithm to consider the shear response.
In order to achieve this, a new damage model has been formulated which allows the damage to be computed and controlled on an individual particle, similar to element-based approaches in finite element analysis. This model is validated against experiments in literature for the impact and penetration of soft materials due to high rate projectiles, primarily using cases with simple geometries. The focus of these simulations is the accuracy of cavity formation due to these impacts, as well as the late-time closure of this cavity.