A new microplane model for non-proportionally multiaxial deformation of shape memory alloys addressing both the martensite transformation and reorientation

A new microplane model is established to predict the non-proportionally multiaxial deformation of pseudoelastic shape memory alloys (SMAs) by considering martensite transformation and reorientation. In each microplane, various martensite variants with certain shear directions are introduced. Adopting the static constraint formulation, the shear and normal stresses in each microplane are obtained through a macroscopic stress tensor. Thermodynamically-consistent kinetic equations of internal variables are derived based on the Clausius's dissipative inequality. Employing the principle of complementary virtual work, a macroscopic strain tensor is obtained by integrating the strains on the microplanes with all orientations. Comparisons between the simulated results and corresponding experimental ones show that the non-proportionally multiaxial deformations of pseudoelastic SMAs can be reasonably predicted. Moreover, the effects of the martensite reorientation and the number of martensite variants on the macroscopic stress-strain responses of pseudoelastic SMAs are discussed.