This 2006 work began with the author's exploration of the
applicability of the finite deformation theory of elasticity when
various standard assumptions such as convexity of various energies
or ellipticity of the field equations of equilibrium are
relinquished. The finite deformation theory of elasticity turns out
to be a natural vehicle for the study of phase transitions in
solids where thermal effects can be neglected. This text will be of
interest to those interested in the development and application of
continuum-mechanical models that describe the macroscopic response
of materials capable of undergoing stress- or temperature-induced
transitions between two solid phases. The focus is on the evolution
of phase transitions which may be either dynamic or quasi-static,
controlled by a kinetic relation which in the framework of
classical thermomechanics represents information that is
supplementary to the usual balance principles and constitutive laws
of conventional theory.
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