On non-equilibrium molecular dynamics with Euclidean objectivity

Abstract

In continuum mechanics, the concept of objectivity requires that the qualitative and quantitative description of physical phenomena remains unchanged under a change in reference frame. It means that the observations in different reference frames are coherent and thus the observed motions can be regarded as objectively equivalent. On the other hand, concerning the material constitution, the principle of material objectivity (also often referred as principle of material frame-indifference, or simply the principle of objectivity) requires that constitutive equations of a material body must be independent of the observer (reference frame). Both objectivity and principle of objectivity have been widely used in modern continuum mechanics studies. However, in molecular dynamics (MD) simulation, which is a prevalent numerical method in nanoscience, consideration is rarely given to the concept of objectivity or principle of objectivity since most of the MD simulations have been performed in inertial systems, where Galilean-invariance is assumed. This research aims to investigate the conditions for Euclidean objectivity in non-equilibrium molecular dynamics (NEMD), where reference frames are non-inertial and multi-physics effects are present in the atomistic material system. By supplementing fictitious acceleration to the governing equation and requiring the principle of objectivity on the constitutive equation, this research arrives at a special solution for NEMD that is Euclidean-invariant. Several sets of simulations demonstrate that equivalent motions can be achieved in NEMD. This study may provide new directions for future MD applications.