Surface energy and microstructure in coherent phase transitions

We study a variational problem involving a nonconvex function of Δu, regularized by a higher order term. The motivation comes from the theory of martensitic phase transformation—specifically, a model for the fine scale structure of twinning near an austenite‐twinned‐martensite interface. It is widely believed that the fine scale structure can be understood variationally, through the minimization of elastic and surface energy. Our problem represents the essence of this minimization. Similar variational problems have been considered by many authors in the materials science literature. They have always assumed, however, that the twinning should be essentially one‐dimensional. This is in general false. Energy minimization can require a complex pattern of twin branching near the austenite interface. There are indications that the states of minimum energy may be asymptotically self‐similar. © 1994 John Wiley & Sons., Inc.