Piecewise affine stress-free martensitic inclusions in planar nonlinear elasticity.

We consider a partial differential inclusion problem which models stress-free martensitic inclusions in an austenitic matrix, based on the standard geometrically nonlinear elasticity theory. We show that for specific parameter choices there exist piecewise affine continuous solutions for the square-to-oblique and the hexagonal-to-oblique phase transitions. This suggests that for specific crystallographic parameters the hysteresis of the phase transformation will be particularly small.