Abstract: In this paper we present energy minimization problems for deformations of materials whose bulk energies have two potential wells. (Two-well models have often been used in simple models of shape memory alloys.) The higher-dimensional models feature relaxed bulk energies derived from double-well potentials with two compatible quadratic wells. The relaxation of the double quadratic well can be calculated explicitly. The relaxed minimization problems are regularized through the use of spatially nonlocal forces. These forces are related to Van der Waals capillary forces and interfacial or coherence forces used in phase fraction theories. We describe an algorithm for computing stationary points of the energy, and do a number of calculations on 1-D static deformations. Our calculations show a rich class of metastable states that form themselves into hysteresis loops and subloops. !16
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