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Improved one-dimensional constitutive model of superelastic shape memory alloy wires

The superelastic shape memory alloys (SMAs) have received increasing interest attributed to their unique mechanical properties. Modeling of SMAs' thermomechanical behavior has been an active area of research; however the existing models are generally valid only for quasi-static loading conditions and extremely complex for practical use. In this research, one-dimensional cyclic loading tests of superelastic shape memory alloy wires are first performed to determine their hysteresis properties. The effects of the strain amplitude and the loading rate on the mechanical properties are studied and formulized by least-square method. Based on the Graesser's model, an improved model is developed. The improved model divides the full loop into three parts: the loading branch, the unloading branch before the completion of the reverse transformation and the elastic unloading branch after the completion of reverse transformation, each part adopts its respective parameters. The improved model not only has the same advantages as the Graesser's model, such as relative simple formulation with parameters that can be easily acquired and being valid for dynamic loading conditions, but also overcomes the deficiency of the Graesser's model, i.e. ignoring the effects of loading path on the model parameters. Numerical simulations are conducted. Comparisons indicate that the improved Graesser's model accurately reflects all the hysteresis characteristics and provides a better prediction of the SMA's actual hyteresis behavior than the Graesser's model at varying levels of strain and loading rate.