On stress calculations in atomistic simulations

Abstract

A systematic comparison between the decomposed virial formula and the Tsai formula shows that they are mathematically equivalent in calculating the overall average stress of an atomistic system. But in the case of calculating local stress distribution, the former gives ambiguous results, e.g. it gives nonzero normal stress at free surfaces and it typically 'underestimates' the inhomogeneity of microstructures and deformations in material. With a highly degenerate atomic chain model, we show mathematically that the results obtained by the decomposed virial formula are accurate only if the deformation is homogeneous within the neighbourhood of an interaction-cutoff radius, centred at the atomic site considered. Thus it is worth noting that the Tsai formula is more adequate for calculating both the overall average stress and local stress distribution. © 2006 IOP Publishing Ltd.