Constitutive modeling of shape memory alloys under cyclic loading considering permanent strain effects

In many applications of shape memory alloys, the structure experiences a cyclic thermomechanical loading. The present work develops a phenomenological constitutive model for permanent strain evolution in shape memory alloys (SMAs) under cyclic loading. To this end, proper internal variables and material parameters together with free energy and limit function are introduced. The model is able to predict hysteresis loop and its changes by evolution of permanent strain. To show the model capability, we calibrate the model and predict two different sets of experiments. Moreover, the proposed model capability in predicting degradation effects as well as evolution rate and stabilization of permanent strain is carefully studied through several parametric studies. Finally, we show that the model and its numerical implementation is capable in multiaxial non-proportional loadings as well as thermal cyclic loading.