Interfacial and inhomogeneity penalties in phase transitions

Non-convex free energies permit phase transitions to occur. The ensuing state of a body is non-homogeneous and endowed with interphase boundaries. Both the inhomogeneity and the interfaces may contribute to the free energy and thus affect the onset of the phase transition. The paper investigates these effects in a one-dimensional setting and for deformation control. The main conclusion is that the incipient phase mixture is characterized by a stable kernel of small but finite phase fraction. This kernel must not be confused with the unstable nucleus whose energy maximum must be overcome before the kernel can form. We consider also the energy landscape of partial equilibria in which the load is uniform but the phase fraction and the number of interfaces have not yet reached equilibrium.