This paper introduces Granular algorithm enhancing Material Point Method (MPM) that allows for simulation of granular flows in the quasi-static state, the moderate flow state and the disconnected flow state. The paper first shows the shortcomings of MPM algorithms in modelling the different states of granular flows. Next, it proposes Granular MPM, an enhancement that explicitly introduces the different states of granular flow into MPM and defines the rules for the transition between those states. Subsequently, the paper gives the algorithm and implementation for Granular MPM. The provided algorithm can enhance the common versions of MPM, including original MPM, Generalised Interpolation Material Point and Convected Particle Domain Interpolation. Finally, the paper evaluates Granular MPM and compares it with other available formulation based on: (i) an examination of the behaviour of granular points on a slope, (ii) a simulation of a granular flow over two disconnected inclined surfaces, (iii) a simulation of a silo filling and (iv) a simulation of Toyoura sand flow experiment. The results of Granular MPM simulations are significantly more realistic when compared to the results obtained by other available MPM formulations. The results also indicate that Granular MPM allows for more accurate replication of steady state flows and reduces the grid dependency of MPM when modelling the disconnected flow state, as the initial contact is independent from the grid size.

本文介绍了颗粒算法增强材料点方法（MPM），该方法可以模拟准静态，中度流状态和非连续流状态下的颗粒流。本文首先展示了MPM算法在建模粒状流的不同状态时的缺点。接下来，它提出了粒度MPM，这是一种增强功能，可将粒度流的不同状态显式引入MPM，并定义这些状态之间转换的规则。随后，给出了粒度MPM的算法和实现。所提供的算法可以增强MPM的通用版本，包括原始MPM，广义插值材质点和对流粒子域插值。最后，本文评估了颗粒状MPM并将其与基于以下各项的其他可用公式进行比较：（i）检查斜坡上的颗粒点的行为，（ii）在两个不相连的倾斜表面上的颗粒流模拟，（iii）筒仓填充的模拟，以及（iv）Toyoura砂流实验的模拟。与其他可用的MPM配方所获得的结果相比，颗粒MPM模拟的结果要真实得多。结果还表明，颗粒MPM可以更精确地复制稳态流，并在对断开的流状态进行建模时减少MPM的网格依赖性，因为初始接触与网格大小无关。（iii）筒仓填充的模拟，以及（iv）Toyoura砂流实验的模拟。与其他可用的MPM配方所获得的结果相比，颗粒MPM模拟的结果要真实得多。结果还表明，颗粒MPM可以更精确地复制稳态流，并在对断开的流状态进行建模时减少MPM的网格依赖性，因为初始接触与网格大小无关。（iii）筒仓填充的模拟，以及（iv）Toyoura砂流实验的模拟。与其他可用的MPM配方所获得的结果相比，颗粒MPM模拟的结果要真实得多。结果还表明，颗粒MPM可以更精确地复制稳态流，并在对断开的流状态进行建模时减少MPM的网格依赖性，因为初始接触与网格大小无关。