  We formulate a phenomenological elasto-plastic theory to describe a solid
undergoing a structural transition from a square (p4mm) to an oblique (p2)
lattice in two dimensions. Within our theory, the components of the strain may
be decomposed additively into separate elastic and plastic contributions. The
plastic strain, produced when the local stress crosses a threshold, is governed
by a phenomenological equation of motion. We investigate the dynamics of shape
of an initially square solid as it is cycled through a transformation protocol
consisting of (1) a quench across the transition (2) deformation by an external
stress and finally (3) reverse transformation back to the parent state. We show
that shape recovery at the end of this cycle depends on crucially on the
presence of plasticity in components of the strain responsible for the
transformation.
