Spatially-varying stress fields can be obtained from atomistic simulations as weighted averages over a phase function that depends on the positions and momenta of the atoms and the interatomic forces between them. However atomistic stress fields exhibit significant nonphysical noise on atomic length scales even under uniform loading conditions. This makes it difficult to obtain accurate stress estimates near atomic-scale defects such as nanocrack tips and dislocation cores. To address this issue, we develop an algorithm to filter noise in the atomistic stress for crystalline materials based on a rigorous stress-invariance condition, which leads to a new class of lattice-dependent weighting functions. Stress fields computed using these weighting functions are identically noise-free under uniform conditions, and have greatly reduced noise in general. The method is demonstrated for three example problems: (1) uniform loading of nickel aluminide, (2) a mode I crack in silicon, and (3) screw and edge dislocation cores in aluminum. The noise filtering algorithm is implemented in MDStressLab++, an open source C++ library for computing atomistic stress fields available online at http://mdstresslab.org.

可以从原子模拟获得空间变化的应力场，将其作为相位函数的加权平均值，该函数取决于原子的位置和动量以及原子之间的原子间力。但是，即使在均匀的载荷条件下，原子应力场在原子长度尺度上仍表现出明显的非物理噪声。这使得难以在原子级缺陷（例如纳米裂纹尖端和位错核）附近获得准确的应力估计。为了解决这个问题，我们开发了一种在严格的应力不变条件下过滤晶体材料原子应力中的噪声的算法。，这导致了一类新的依赖于网格的加权函数。使用这些加权函数计算出的应力场在均匀条件下完全没有噪声，并且总体上大大降低了噪声。该方法针对三个示例问题进行了演示：（1）铝化镍的均匀加载；（2）硅中的I型裂纹；（3）铝中的螺钉和位错核。噪声过滤算法在MDStressLab ++中实现，MDStressLab ++是一个开放的C ++库，用于计算原子应力场，可从http://mdstresslab.org在线获得。