Many alloys display the shape-memory effect in single crystal form, ho
wever the degree to which they retain this effect in polycrystalline f
orm varies widely. We propose a theoretical explanation for this diffe
rence, showing that the recoverable strain of a polycrystal depends on
the texture of the polycrystal, the transformation strain of the unde
rlying martensitic transformation and especially critically on the cha
nge of symmetry during the underlying transformation. Roughly, we find
that the greater the change in symmetry during transformation, the gr
eater the recoverable strain. Our results agree with experimental obse
rvations, and provide guidance for the improvement of the shape-memory
effect in polycrystals.