Research

Stress is a fundamental quantity in mechanics and is essential when analyzing macroscopic structures.  The concept of stress originated from ideas in continuum mechanics and is considered a primitive in that setting.  As our ability to construct and manipulate nano-scale structures has improved, understanding the role of stress at the atomic scale has become essential.  In particular in a molecular dynamics setting, we would like to know how to compute stress based on atomic coordinates and momenta since continuum quantities such as strain are ill-defined in discrete media.  Although researchers have been employing the so-called Viral Stress at the atomic scale, a rigorous and consistent derivation of stress based on atomic coordinates and momenta has proven elusive.  Further more, numerical results showing the validity of the Virial Stress are lacking.  In the current work, we present a mathematically rigorous derivation of the Virial Stress and numerical results which support this measure of stress at the atomic scale.  We consider simulations of thermal expansion, both free and constrained, as well as embedded inclusions for Lennard-Jones solids.