Local stresses and elastic constants at the atomic scale

In this paper, we examine the problem of deriving local stress measures and associated elastic constants for a region containing a fixed number of atoms that, is part of a larger body. By means of an expansion of the local interatomic potential energy, we derive expressions for the local second Piola-Kirchoff stress and the associated elastic constants. We relate these to other previously derived atomic scale stress measures. Numerical calculations are presented for the case of an oversized inclusion embedded in an otherwise perfect face-centred cubic crystal.