  Many biological and engineering materials have nonperiodic microstructures
for which classical periodic homogenization results do not apply. Certain
nonperiodic microstructures may be approximated by locally periodic
microstructures for which homogenization techniques are available. Motivated by
the consideration that such materials are often anisotropic and can posses
residual stresses, a broad class of locally periodic microstructures is
considered and the resulting effective macroscopic equations are derived. The
effective residual stress and effective elasticity tensor are determined by
solving unit cell problems at each point in the domain. However, it is found
that for a certain class of locally periodic microstructures, solving the unit
cell problems at only one point in the domain completely determines the
effective elasticity tensor.
