应力和柯西应力的微观公式之间的区别的起源
The origin of the distinction between microscopic formulas for stress and Cauchy stress
摘要：
应力是在原子模拟中常规计算的。然而，从经典力学或量子力学导出的广泛使用的微观应力公式与柯西应力的概念不同，即，真正的机械压力这项工作研究了各种原子应力公式及其不一致性。利用标准的数学定理和力学定律，证明了柯西应力是由内力密度定义的明确结果，从而消除了长期以来对柯西应力基本性质的原子论基础的混淆，并导出了一个新的原子论应力公式，它具有明确的物理意义和明确的数值，满足守恒定律，与柯西应力的概念完全一致。
英文摘要：
Stress is calculated routinely in atomistic simulations. The widely used microscopic stress formulas derived from classical or quantum mechanics, however, are distinct from the concept of Cauchy stress, i.e., the true mechanical tress. This work examines various atomistic stress formulations and their inconsistencies. Using standard mathematic theorems and the law of mechanics, we show that Cauchy stress results unambiguously from the definition of internal force density, thereby removing the long-standing confusion about the atomistic basis of the fundamental property of Cauchy stress, and leading to a new atomistic formula for stress that has clear physical meaning and well-defined values, satisfies conservation law, and is fully consistent with the concept of Cauchy stress.
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