Thermomechanical modeling of hysteresis in SMAs using the dissipationless reference response

The main objective of this study is to introduce a 'dissipationless band' to model inner hysteresis loops of response of shape memory alloys (SMAs). Dissipation that occurs when the material undergoes phase transformation is critical to the modeling of hysteretic behavior. Emphasis is placed on modeling such dissipation in the proposed methodology. Using a dissipationless virtual response of the material, a logical framework for the onset transformation under reversal of cycles is presented. Characteristics of the material transformation with reference to a dissipationless band model the true inner hysteresis loops. It is identified that this dissipationless band occurs due to the difference between the starting states of forward and reverse transformations. The construction of the generalized driving force for the transformation along with the rate of dissipation function is formulated. A numerical example is presented to highlight the qualitative prediction capabilities of the model. The example involves simulating hysteresis loops for different kinds of partial and complete loading cycles in the pseudoelastic state of the material. The predictions show that the proposed one-dimensional model is capable of representing the actual hysteresis behavior of the stabilized shape memory alloys, by effectively incorporating the dissipation effects due to the loading history. © IOP Publishing Ltd.