Summary A central open problem in the study of shape memory polycrystals is the prediction of their recoverable strains. Solving this problem requires an understanding of the possible stress and strain fields that arise in such polycrystals. For polycrystals made of materials undergoing cubic-tetragonal transformations, we show that the strains fields associated with macroscopic recoverable strains are related to the solutions of hyperbolic partial differential equations. We explore consequences of this relationship and connections to previous conjectures characterizing polycrystals with non-trivial recoverable strains. We also show that stress fields in shape memory polycrystals could be concentrated on lower-dimensional surfaces (planes and lines). We do this by proving a dual variational characterization of recoverable strains and presenting several examples. Implications of this characterization for effective properties and the development of numerical methods are discussed.
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