HYDRODYNAMIC DESCRIPTION OF ELASTIC SOLIDS WITH OPEN BOUNDARY-CONDITIONS UNDERGOING A PHASE-TRANSITION

We present a thorough examination of the deterministic dynamics of finite, nonlinear, continuum systems which undergo elastic phase transitions. Particular attention is given to the correct implementation of open boundary conditions, which are nontrivial. As examples of the application of this formalism, in this paper we model two transformations: (i) The symmetry-preserving change of volume first-order transition undergone by some mixed-valence compounds, such as Ce1-xThx. This example allows us to demonstrate how a bulk fluctuation that is subcritical (viz., does not nucleate product phase) can propagate to the surface and become supercritical (viz., does nucleate the transformed state) due to the greatly reduced nucleation barrier found at the system's only heterogeneity, its surface. (ii) The late-stage dynamics of autocatalytic twinning undergone by shear martensites, such as discussed by Bales and one of us in Phys. Rev. Lett. 67, 3412 (1991). Such complete dynamical systems of equations involving a small number of continuum fields are a prerequisite for examining the rich sequences of patterns that form at these and other first-order transitions involving strains.