How to compute the atomic stress objectively
How to compute the atomic stress objectively
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DOI：
10.1166/jctn.2009.1148
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发表时间：
2008-10
期刊：
影响因子：
--
通讯作者：
B. Liu;X. Qiu
中科院分区：
文献类型：
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作者：
B. Liu;X. Qiu
原子模拟一直是力学研究中强有力的研究工具，但如何客观地计算相当于柯西应力的原子应力仍然存在争议，特别是在维里应力定义中与速度相关的部分。本文严格遵循连续介质柯西应力的经典定义，提出了基本的拉格朗日原子应力，可用于在任何情况下获得正确的柯西应力。此外，提出了拉格朗日维里应力，它仍然是维里形式，但不包括速度，以避免有争议的速度处理。研究还发现，广泛使用的经典维里应力实际上是欧拉维里应力，其中包括原子速度，并且仅当脉冲动量定理适用于估计内力时才有效。然而，在实际情况中，例如旋转中的材料体积单元和本文中提出的示例，对欧拉原子应力的这一要求并不总是能够满足，但是所提出的拉格朗日原子应力可以避免这些与速度相关的非客观性。
Atomistic simulation has been a powerful study tool in mechanics research, but how to objectively compute the atomic stress equivalent to Cauchy stress is still controversial, especially on the velocity-related part in the virial stress definition. In this paper, by strictly following the classical definition of the Cauchy stress for continuum medium, the fundamental Lagrangian atomic stress is proposed and can be used to obtain the correct Cauchy stress under any circumstances. Furthermore, the Lagrangian virial stress is proposed, which is still in virial form but does not include velocities to avoid controversial velocity treatments. It is also found that the widely used classical virial stress is actually the Eulerian virial stress, which includes the velocities of atoms, and is valid only when the impulse-momentum theorem is applicable to estimate the internal forces. However this requirement for the Eulerian atomic stress can not always be met in practical cases, such as the material volume element in rotation and the examples presented in this paper, but the proposed Lagrangian atomic stress can avoid these velocity-related nonobjectivities.