  We present a time-dependent Ginzburg-Landau model of nonlinear elasticity in
solid materials. We assume that the elastic energy density is a periodic
function of the shear and tetragonal strains owing to the underlying lattice
structure. With this new ingredient, solving the equations yields formation of
dislocation dipoles or slips. In plastic flow high-density dislocations emerge
at large strains to accumulate and grow into shear bands where the strains are
localized. In addition to the elastic displacement, we also introduce the local
free volume {\it m}. For very small $m$ the defect structures are metastable
and long-lived where the dislocations are pinned by the Peierls potential
barrier. However, if the shear modulus decreases with increasing {\it m},
accumulation of {\it m} around dislocation cores eventually breaks the Peierls
potential leading to slow relaxations in the stress and the free energy
(aging). As another application of our scheme, we also study dislocation
formation in two-phase alloys (coherency loss) under shear strains, where
dislocations glide preferentially in the softer regions and are trapped at the
interfaces.
