Time integration and assessment of a model for shape memory alloys considering multiaxial nonproportional loading cases

The paper presents a numerical implementation of the ZM model for shape memory alloys (Zaki and Moumni, 2007a) that fully accounts for nonproportional loading and its influence on martensite reorientation and phase transformation. Detailed derivation of the time-discrete implicit integration algorithm is provided, including an explicit closed-form expression for the continuous material jacobian. The algorithm is used for finite element simulations using Abaqus, in which the model is implemented by means of a user material subroutine. Extensive validation of the model is provided against multiple sets of experimental and numerical simulation data taken from the literature.