Finite-strain micromechanical model of stress-induced martensitic transformations in shape memory alloys

A micromechanical model of stress-induced martensitic transformation in single crystals of shape memory alloys is developed. This model is a finite-strain counterpart to the approach presented recently in the small-strain setting [S. Stupkiewicz, H. Petryk, J. Mech. Phys. Solids 50 (2002) 2303–2331]. The stress-induced transformation is assumed to proceed by the formation and growth of parallel martensite plates within the austenite matrix. Propagation of phase transformation fronts is governed by a rate-independent thermodynamic criterion with a threshold value for the thermodynamic driving force, including in this way the intrinsic dissipation due to phase transition. This criterion selects the initial microstructure at the onset of transformation and governs the evolution of the laminated microstructure at the macroscopic level. A multiplicative decomposition of the deformation gradient into elastic and transformation parts is assumed, with full account for the elastic anisotropy of the phases. The pseudoelastic behavior of Cu–Zn–Al single crystal in tension and compression is studied as an application of the model.