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.

离散和连续计算方法通常都用于基于模型的故障演化仿真。分子动力学（MD）和有限元方法（FEM）分别是代表性的离散粒子方法和连续方法。质点法（MPM）是基于连续体的粒子法，它基于控制方程的弱形式以类似于FEM的方式制定。在这里，我们报告了由全原子MD，粗粒MD（其中几个原子归为一个有效粒子）和MPM预测的剪切带演化的比较研究。总结了不同尺度响应的总体特征，并讨论了通过三种空间离散化方法获得的结果之间的异同。