Arun K. Subramaniyan and C. T. Sun, accepted for publication in International Journal of Solids and Structures, doi:10.1016/j.ijsolstr.2008.03.016

The equivalence of the virial stress and Cauchy stress is reviewed
using both theoretical arguments and numerical simulations. Using
thermoelasticity problems as examples, we numerically demonstrate that
virial stress is equivalent to the continuum Cauchy stress. Neglecting
the velocity terms in the definition of virial stress as many authors
have recently suggested, can cause significant errors in interpreting
MD simulation results at elevated temperatures (T > 0 K).

Calculating stresses in MD simulations is a controversial topic. There are two different schools of thought about the equivalence of the virial stress to the continuum Cauchy stress; for and against. Some argue based on momentum balance, that only the potential contribution to the virial stress should be considered as the continuum Cauchy stress. However, others assert that the total virial stress that contains both the kinetic and potential parts is indeed the quantity that corresponds to the Cauchy stress in continuum mechanics. We used a simple thermo-elastic analysis to verify the validity of using the total virial stress as the continuum Cauchy stress and found that the total virial stress is indeed the continuum Cauchy stress.