  Irreversible plastic forming of B19$^\prime$ martensite of the NiTi shape
memory alloy is discussed within the framework of continuum mechanics. It is
suggested that the main mechanism arises from coupling between martensite
reorientation and coordinated $[100](001)_{\rm M}$ dislocation slip. A
heuristic model is proposed, showing that the ${(20\bar{1})_{\rm M}}$
deformation-twin bands, commonly observed in experiments, can be interpreted as
a combination of dislocation-mediated kink bands, appearing due to strong
plastic anisotropy, and reversible twinning of martensite. We introduce a term
'kwinking' for this combination of reversible twinning and irreversible plastic
kinking. The model is subsequently formulated using the tools of nonlinear
elasticity theory of martensite and crystal plasticity, introducing 'kwink
interfaces' as planar, kinematically compatible interfaces between two
differently plastically slipped variants of martensite. It is shown that the
${(20\bar{1})_{\rm M}}$ kwink bands may be understood as resultsing from energy
minimization, and that their nucleation and growth and their pairing with
$(100)_{\rm M}$ twins into specific patterns enables low-energy plastic forming
of NiTi martensite. We conclude that kwinking makes plastic deformation of
B19$^\prime$ martensite in polycrystalline NiTi possible despite only one slip
system being available.
