  In this work we present a formalism for the calculation of the local elastic
constants in inhomogeneous systems based on a method of planes. Unlike previous
work, this formalism does not require the partitioning of the system into a set
of finite volumes over which average elastic constants are calculated. Results
for the calculation of the local elastic constants of a nearest neighbor
Lennard-Jones fcc crystal in the bulk and in a thin film are presented. The
local constants are calculated at exact planes of the (001) face of the
crystal. The average elastic constants of the bulk system are also computed and
are consistent with the local constants. Additionally we present the local
stress profiles in the thin film when a small uniaxial strain is applied. The
resulting stress profile compares favorably with the stress profile predicted
via the local elastic constants. The surface melting of a model for argon for
which experimental and simulation data are available is also studied within the
framework of this formalism.
