Single-and multi-velocity formulations for impact and pulverization

Material interaction is often numerically modeled using a single-velocity field, if material pulverization or the subsequent debris flow is not a concern. To consider pulverization and the subsequent debris flow, one needs to switch to a multi-velocity or multi-phase formulation at some point in the numerical process because of the scale of the debris particles. But when and how to switch are significant issues. This paper shows that a combination of a multi-velocity formulation based on an ensemble averaging method and the material point method can be used to describe the entire material interaction process and to avoid the switching of the descriptions. Although physical models for the multi-velocity formulation are still subjects of active research, this paper shows a set of impact and pulverization problems that can be studied with a simple multi-velocity model. This paper also examines the differences between the material interface treatments in the single and multi-velocity formulations, while comparing the advantages and disadvantages of the formulations. Numerical results obtained from single and multi-velocity formulations are in good agreement with experimental data. The numerical examples show that the combination of the multi-velocity formulation and the recently improved material point method has significant advantages in numerical simulations of impact and pulverization problems. It is hoped that this new capability will help and encourage the development of high fidelity material interaction models.