Nano-scale stress: From discrete to continuum

The present work deals with a stress measure derived from a general atomic force field. Usually, stresses at atomic level are determined through the Clausius virial theorem for a fixed volume containing interacting particles. The present stress is derived on the basis of the first Brillouin zone, or equivalently the Voronoi cell, surrounding the atom. Thus, this is the smallest scale at which the stress measure makes sense. Obviously, the stress is discrete in nature since the Voronoi cells are discrete. In order for the stress to become continuous the finite element formalism is used in terms of interpolation functions from 3D Voronoi elements. The present stress measure is non-local, it is not necessarily symmetric in its indices and incorporates micro-deformations.