Comparative investigation of shear-band evolution using discrete and continuum-based particle methods

Both discrete and continuous computational methods are commonly used for model-based simulation of failure evolution. Molecular dynamics (MD) and the finite element method (FEM) are representative discrete particle and continuous methods, respectively. The Material Point Method (MPM) is a continuum-based particle method that is formulated based on the weak form of the governing equations in a way similar to the FEM. Here, we report a comparative study of shear-band evolution as predicted by all-atom MD, coarse-grain MD (in which several atoms are subsumed into a single effective particle), and MPM. Overall features of the responses at different scales are summarized, along with a discussion of similarities and differences among the results obtained via the three spatial discretization approaches. This work could serve as a benchmark example for developing multiscale geomechanics under extreme loading scenarios such as earth penetration and underground explosions.