The role of the spinodal region in one-dimensional martensitic phase transitions

摘要

A common approach in modeling martensitic phase transitions in the framework of continuum mechanics involves a nonconvex energy. This paper analyzes the influence of the spinodal region, or the region where the energy density is concave, on the resulting equilibria. We compare a one-dimensional model with a degenerate spinodal region to models with a finite spinodal region. In all models we consider an elastic bar with a nonconvex energy placed on a rigid elastic foundation, to mimic elastic interactions between different phases in higher dimensions. Interfacial energy is modeled by a strain-gradient term, We find that when the spinodal region is small, global minima are not affected, and the minimum energy as a function of the overall strain exhibits nonsmooth oscillations associated with sudden finite phase nucleation. However, a sufficiently wide spinodal region results in the partial smoothening of the global minimum energy and infinitesimal phase nucleation in the interior of the bar. This involves gradual growth of a pretransitional nucleus with strain in the spinodal region. We show a hysteresis path using an energetic strategy of switching between branches of local minima. Copyright (C) 1998 Elsevier Science B.V. [References: 32]