  We present a unified variational treatment of evolving configurations in
crystalline solids with microstructure. The crux of our treatment lies in the
introduction of a vector configurational field. This field lies in the
material, or configurational, manifold, in contrast with the traditional
displacement field, which we regard as lying in the spatial manifold. We
identify two distinct cases which describe (a) problems in which the
configurational field's evolution is localized to a mathematically sharp
interface, and (b) those in which the configurational field's evolution can
extend throughout the volume. The first case is suitable for describing
incoherent phase interfaces in polycrystalline solids, and the latter is useful
for describing smooth changes in crystal structure and naturally incorporates
coherent (diffuse) phase interfaces. For sharp interfaces that are
out-of-equilibrium, the second law of thermodynamics furnishes restrictions on
the kinetic law for the interface velocity. The class of problems in which the
material undergoes configurational changes between distinct, stable crystal
structures are characterized by free energy density functions that are
non-convex with respect to configurational strain. For physically meaningful
solutions and mathematical well-posedness, it becomes necessary to incorporate
interfacial energy. This we have done by introducing a configurational strain
gradient dependence in the free energy density function following ideas laid
out by Toupin (Arch. Rat. Mech. Anal. 11, 1962, 385-414). The variational
treatment leads to a system of partial differential equations governing the
configuration that is coupled with the traditional equations of nonlinear
elasticity. Numerical examples are presented to demonstrate interface motion as
well as evolving microstructures of crystal structures.
