  The dynamics of sharp interfaces separating two non-hydrostatically stressed
solids is analyzed using the idea that the rate of mass transport across the
interface is proportional to the thermodynamic potential difference across the
interface. The solids are allowed to exchange mass by transforming one solid
into the other, thermodynamic relations for the transformation of a mass
element are derived and a linear stability analysis of the interface is carried
out. The stability is shown to depend on the order of the phase transition
occurring at the interface. Numerical simulations are performed in the
non-linear regime to investigate the evolution and roughening of the interface.
It is shown that even small contrasts in the referential densities of the
solids may lead to the formation of finger like structures aligned with the
principal direction of the far field stress.
