A stress analysis method for molecular dynamics systems

Abstract

As the development of micro/nanoelectromechanical devices continues at a fast pace, there is a growing need to bridge the gap between material behavior at the atomic and molecular levels and material behavior at length scales relevant to most engineering and industrial applications. Since stress is one of the most fundamental quantities in continuum mechanics (CM), it is desirable to introduce stress methods that are applicable to both continuum and discrete systems, such as those modeled by molecular dynamics (MD). Thus, the objective of this study was to demonstrate how a traction vector-based stress method that is compatible with CM can be used to examine MD systems of crystalline solids undergoing small lattice distortion. In the bulk of face-centered-cubic (FCC) and body-centered-cubic solids, the traction vector-based atomic stress definition used in this study is shown to be equivalent to the classical energy-based virial stress that is commonly used for small deformations and low temperatures, i.e., negligible thermal vibration. However, contrary to the virial stress, the components of the present atomic stress diminish in the region close to a free surface, consistent with the traction-free boundary condition. The validity of the stress method developed herein is demonstrated by MD results of the bulk modulus of FCC copper, the surface tension of an FCC solid, and the subsurface stress field of an FCC half-space indented by a rigid flat punch.