  In many processes for crystalline materials such as precipitation,
heteroepitaxy, alloying, and phase transformation, lattice expansion or
compression of embedded domains occurs. This can significantly alter the
mechanical response of the material. Typically, these phenomena are studied
macroscopically, thus neglecting the underlying microscopic structure. Here we
present the prototypical case of an elastic inclusion described by a mesoscale
model, namely a coarse-grained phase-field crystal model. A spatially-dependent
parameter is introduced into the free energy functional to control the local
spacing of the lattice structure, effectively prescribing an eigenstrain. The
stress field obtained for an elastic inclusion in a 2D triangular lattice is
shown to match well with the analytic solution of the Eshelby inclusion
problem.
