Multiscale Modeling &Simulation, Volume 19, Issue 2, Page 1066-1082, January 2021.
In particulate systems, the ensemble average accounting for effects from all particles is expressed as the expected value related to the nearest particle probability. Using this expression, a stress is defined even for long-range particle interactions without the divergence difficulty because of the rapid far field decay of the probability. Similar to the potential part of the virial stress in molecular systems, this stress represents particle--particle interactions through the surrounding field. As examples, the stresses are calculated for systems of charged particles and disperse multiphase flows.

中文翻译：

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来自颗粒系统中长程相互作用的应力

多尺度建模与仿真，第 19 卷，第 2 期，第 1066-1082 页，2021
年1 月。在微粒系统中，考虑所有粒子影响的整体平均值表示为与最近粒子概率相关的预期值。使用这个表达式，即使对于远距离粒子相互作用，也可以定义应力，而不会因为概率的快速远场衰减而产生发散困难。类似于分子系统中潜在的力应力部分，这种应力代表粒子-粒子在周围场中的相互作用。例如，计算带电粒子系统和分散多相流的应力。