“…Martensite appears in the form of several variants with different orientations with respect to the austenite parent crystal, and therefore different characteristic transformation strains (Bain strains) are resulted (Ball and James, 1989; M. Pitteri and Zanzotto, 1998;James and Hane, 2000;Pitteri and Zanzotto, 2002;Bhattacharya, 2003). According to equilibrium thermomechanics (Ericksen, 1975;Falk, 1980;James, 1980;Abeyaratne and Knowles, 1991;He and Sun, 2009;Duval et al, 2011;Hallai and Kyriakides, 2013) and the experimental observations (Segui et al, 1996;Glatz et al, 2009;Seiner, 2015;Zhang et al, 2020;Qin et al, 2023;Zhang et al, 2023), the martensite variants and austenite with equal free energy can coexist during the phase transformation, among which there are twin boundaries (separating different martensite variants) and habit planes (separating austenite from martensite twins or variants). To guarantee the deformation reversibility of the phase transformation (avoiding plasticity), the twin boundaries and the habit planes must be compatible (coherent), meaning that the characteristic transformation strains of the different domains (martensite variants, twins, and austenite) must be accommodated without elastic strain (called "perfectly compatible" domain patterns) or with only small elastic strains (so-called "non-perfectly compatible" domain patterns).…”