Rigelesaiyin Ji, Diaz Adrian, Li Weixuan, Xiong Liming, Chen Youping
Department of Aerospace Engineering, Iowa State University, Ames, IA 50011, USA.
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA.
Proc Math Phys Eng Sci. 2018 Sep;474(2217):20180155. doi: 10.1098/rspa.2018.0155. Epub 2018 Sep 5.
The stress tensor is described as a symmetric tensor in all classical continuum mechanics theories and in most existing statistical mechanics formulations. In this work, we examine the theoretical origins of the symmetry of the stress tensor and identify the assumptions and misinterpretations that lead to its symmetric property. We then make a direct measurement of the stress tensor in molecular dynamics simulations of four different material systems using the physical definition of stress as force per unit area acting on surface elements. Simulation results demonstrate that the stress tensor is asymmetric near dislocation cores, phase boundaries, holes and even in homogeneous material under a shear loading. In addition, the atomic virial stress and Hardy stress formulae are shown to significantly underestimate the stress tensor in regions of stress concentration.
在所有经典连续介质力学理论以及大多数现有的统计力学公式中，应力张量都被描述为对称张量。在这项工作中，我们研究了应力张量对称性的理论根源，并确定了导致其对称性质的假设和误解。然后，我们利用应力作为作用在表面元上的单位面积力的物理定义，在四个不同材料系统的分子动力学模拟中直接测量应力张量。模拟结果表明，在位错核心、相界、孔洞附近，甚至在剪切载荷作用下的均匀材料中，应力张量都是不对称的。此外，原子维里应力和哈代应力公式在应力集中区域被证明会显著低估应力张量。
