Thermomechanical description of shape memory alloys using constitutive models with assumed polynomial phase transformation kinetics

Shape memory alloys present remarkable thermomechanical behaviors due to solid phase transformations. The complexity of the involved phenomena makes the constitutive modeling of this class of smart material a challenging subject. Considering the different approaches presented in the literature, the constitutive models with assumed phase transformation kinetics are popular, achieving reasonable results. This paper deals with one-dimensional constitutive models that employs a novel strategy to describe phase transformation kinetics using polynomial functions. Three different polynomial functions are treated: linear, quadratic, and cubic. Besides, the novel approach defines the phase transformation surfaces in such a way that allows the description of new phenomena including tension-compression behaviors and two-way shape memory effect. Experimental data compiled from the literature guides the investigation treating temperature-induced phase transformation; pseudoelasticity; one-way and two-way shape memory effects; internal subloops due to incomplete phase transformations. Numerical simulations are carried out comparing the novel functions with the classical cosine function. Results indicate that the model with polynomial phase transformation kinetics is able to capture the main features of SMA thermomechanical behavior. The investigation shows that the cubic polynomial is equivalent to the cosine function and the linear polynomial presents good estimations, being related to low computational cost since it avoids iterative approaches for strain-driven cases.