“…For the past decades several constitutive models have appeared within the literature (e.g., Raniecki et al, 1992;Abeyaratne and Knowles, 1993;Ivshin and Pence, 1994;Boyd and Lagoudas, 1996;Lubliner and Auricchio, 1996;Panoskaltsis et al, 2004), which within the context of a geometrical linear theory can capture several aspects of the experimentally observed response. Nevertheless, the physics of the problem (e.g., see Smallman and Bishop, 2000), together with some basic results of the crystallographic theory of martensitic phase transformations (e.g., Ball and James, 1987;James and Hane, 2000;Abeyaratne et al 2001), suggest that a geometrically non -linear approach is more appropriate. Levitas and Preston, (2005) discuss the drawbacks of the infinitesimal models and they report that finite rotations of the crystal lattice can occur at small transformation strains (small strains and finite rotations) and can crucially affect the phase transformation conditions.…”