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We study convex integration solutions in the context of the modelling ofshape-memory alloys. The purpose of the article is two-fold, treating bothrigidity and flexibility properties: Firstly, we relate the maximal regularityof convex integration solutions to the presence of lower bounds in variationalmodels with surface energy. Hence, variational models with surface energy couldbe viewed as a selection mechanism allowing for or excluding convex integrationsolutions. Secondly, we present the first numerical implementations of convexintegration schemes for the model problem of the geometrically linearisedtwo-dimensional hexagonal-to-rhombic phase transformation. We discuss andcompare the two algorithms from [RZZ16] and [RZZ17].

Convex Integration Arising in the Modelling of Shape-Memory Alloys: Some Remarks on Rigidity, Flexibility and Some Numerical Implementations