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Surface energy and microstructure in coherent phase transitions
Author(s) -
Kohn Robert V.,
Müller Stefan
Publication year - 1994
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160470402
Subject(s) - crystal twinning , energy minimization , minification , martensite , austenite , surface energy , phase (matter) , elastic energy , mathematics , statistical physics , scale (ratio) , length scale , microstructure , materials science , mathematical optimization , thermodynamics , physics , mechanics , metallurgy , quantum mechanics
We study a variational problem involving a nonconvex function of Δ u , 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.