  We study the branching of twins appearing in shape memory alloys at the
interface between austenite and martensite. In the framework of
three-dimensional non-linear elasticity theory, we propose an explicit,
low-energy construction of the branched microstructure, generally applicable to
any shape memory material without restrictions on the symmetry class of
martensite or on the geometric parameters of the interface. We show that the
suggested construction follows the expected energy scaling law, i.e., that (for
the surface energy of the twins being sufficiently small) the branching leads
to energy reduction. Furthermore, the construction can be modified to capture
different features of experimentally observed microstructures without violating
this scaling law. By using a numerical procedure, we demonstrate that the
proposed construction is able to predict realistically the twin width and the
number of branching generations in a Cu-Al-Ni single crystal.
