Atomic-level Stress Calculation and Continuum-Molecular System Equivalence

An atomistic level stress tensor is defined with physical clarity, based on the SPH method. This stress tensor rigorously satisfies the conservation of linear momentum, and is appropriate for both homogeneous and inhomogeneous deformations. The formulation is easier to implement than other stress tensors that have been widely used in atomistic analysis, and is validated by numerical examples. The present formulation is very robust and accurate, and will play an important role in the multiscale simulation, and in molecular dynamics. An equivalent continuum is also defined for the molecular dynamics system, based on the developed definition of atomistic stress and in conjunction with the SPH technique. The process is simple and easy to implement, and the fields are with high-order continuity. This equivalent continuum maintains the physical attributes of the atomistic system. This development provides a systematic approach to the continuum analysis of the discrete atomic systems. keyword: Atomistic analysis, stress, SPH, continuum.