An approach to bridge atomic- and continuumstress

A framework for calculating the non-local, asymmetric atomic stress has been developed. The approach is based on the assumption that stress is derivable from an energy expression, i.e. an atomic force field. The atomic stress is linked to the first Brillouin zone or equivalently 3D Voronoi element surrounding the atom. Atomic displacements from e.g. MD simulations are used as input to the framework. The discrete nature of the atomic scale is linked to continuum theory through the Finite Element formalism using the interpolation functions of 3D Voronoi elements. The advantage of this approach compared to using the Clausius virial theorem is that the stresses from the present approach is defined in the same way as the nonlocal stress of traditional continuum mechanics so the relation of the present atomic stress and the traditional Cauchy stress is strongly anticipated but remains to be proved.