A phenomenological SMA model for combined axial–torsional proportional/non-proportional loading conditions

In this paper, a simple and robust phenomenological model for shape memory alloys (SMAs) is proposed to simulate main features of SMAs under uniaxial as well as biaxial combined axial–torsional proportional/non-proportional loadings. The constitutive model for polycrystalline SMAs is developed within the framework of continuum thermodynamics of irreversible processes. The model nominates the volume fractions of self-accommodated and oriented martensite as scalar internal variables and the preferred direction of oriented martensitic variants as directional internal variable. An algorithm is introduced to develop explicit relationships for the thermo-mechanical behavior of SMAs under uniaxial and biaxial combined axial–torsional proportional/non-proportional loading conditions and also thermal loading. It is shown that the model is able to simulate main aspects of SMAs including self-accommodation, martensitic transformation, orientation and reorientation of martensite, shape memory effect, ferro-elasticity and pseudo-elasticity. A description of the time-discrete counterpart of the proposed SMA model is presented. Experimental results of uniaxial tension and biaxial combined tension–torsion non-proportional tests are simulated and a good qualitative correlation between numerical and experimental responses is achieved. Due to simplicity and accuracy, the model is expected to be used in the future studies dealing with the analysis of SMA devices in which two stress components including one normal and one shear stress are dominant.