Deformation of polydomain crystalline materials consisting of domains of di
fferent phases or domains of differently oriented areas of the same phase a
re considered. These polydomain materials are adaptive if their domain micr
ostructure can change in response to a change of external mechanical or ele
ctrical fields. For ferroelastic and martensitic transformations in shape m
emory alloys the domain interfaces are so mobile that the deformation is al
most reversible. Therefore, it can be treated as a superelastic deformation
which is additional to the elastic one. Thermodynamic analysis of the evol
ution of an equilibrium microstructure has shown that the mechanical behavi
or of a transforming crystal is in principle different for displacement con
trolled deformation and for load controlled deformation. The different type
s of the microstructure are considered: (1) a heterophase polydomain; (2) a
heterostructures containing besides an adaptive component, a passive compo
nent which remains unchangeable during the deformation.