STABILITY OF A 2-PHASE PROCESS IN AN ELASTIC SOLID

This work investigates the linear stability of an antiplane shear motion which involves a steadily propagating normal planar phase boundary in an arbitrary element of a family of non-elliptic generalized neo-Hookean materials. It is shown that such a process is linearly unstable with respect to a large class of disturbances if and only if the kinetic response function-a constitutively supplied entity which relates the normal velocity of a phase boundary to the driving traction which acts on it-is locally decreasing as a function of the appropriate argument. This result holds whether or not inertial effects are taken into consideration, demonstrating that the linear stability of the relevant process depends entirely upon the transformation kinetics intrinsic to the kinetic response function. The morphological evolution of the interface is then, in an inertia-free setting, tracked for a short time subsequent to the perturbation. It is found that, when the kinetic response function is non-monotonic, the phase boundary can evolve so as to qualitatively resemble the plate-like structures which are found in displacive solid-solid phase transformations.