Equations and closure models for material pulverization and debris flow

A transition from interacting continua to a disperse debris flow is numerically simulated using a multi-velocity formulation based on the ensemble phase average. The numerical calculation takes advantage of the recently developed dual domain material point method, which overcomes numerical instabilities, numerical diffusion and mesh distortion issues encountered in other numerical methods in cases of large material deformations. Comparisons with experiments show that the difference between the average of the velocity gradient and the gradient of the average velocity is important. To consider the transition from a continuum motion to a disperse flow, a model for this difference is expressed in terms of the effective plastic strain and the critical strain of the material. Although the model results in excellent comparisons to the experimental results, more work to study the difference and the model is needed for broader applications.