  We present a theoretical method for deriving the macroscopic stress tensor
and elastic response of ordered systems within a Ginzburg-Landau type density
field theory. This is based on spatially coarse graining the microscopic stress
which is determined by the variational of a free energy with respect to mass
displacements. We find simple expressions for the stress tensor for phase field
crystal (PFC) models for different crystal symmetries in two and three
dimensions. Using tetradic product sums of reciprocal lattice vectors, we
calculate elastic constants and show that they are directly related to the
symmetries of the reciprocal lattices. This allows us to formulate a new PFC
model for simple cubic ordering and determine its elastic properties. We also
show that except for bcc lattices, there are regions of model parameters for
which the elastic response is isotropic. The predicted elastic stress-strain
curves are verified by numerical strain-controlled bulk and shear deformations.
The method extends also to defected crystals which we exemplify by considering
an edge and screw dislocation in the simple cubic lattice.
