A three-dimensional constitutive model for shape memory alloy considering transformation-induced plasticity, two-way shape memory effect, plastic yield and tension-compression asymmetry

In this paper, a three-dimensional phenomenological constitutive model for shape memory alloys (SMA) is proposed with consideration given to various thermomechanical mechanisms. This model includes, for the first time in literature, the major mechanisms influencing the behaviors of SMA actuators in a unified thermodynamics framework: transformation-induced plasticity (TRIP), two-way shape memory effect (TWSME), plastic yield as well as tension-compression asymmetry. Furthermore, a new method to address the characteristics of transformation strain varying with stress levels was proposed. Moreover, a new transformation hardening function was proposed which can give a more accurate prediction of the transformation process. The three-dimensional constitutive model is solved using return mapping algorithm for an increment in a material point in the form of strain and temperature increment. The complete algorithm is proposed and the user-defined material subroutine (UMATs) for finite element problem is established. To validate the proposed SMA constitutive model, the parameters of the SMA material are determined through uniaxial tensile tests. The SMA tubes of the same material are used to conduct both experiments and simulation, with tension-compression asymmetry considered. Training experiments and simulations have been carried out on the SMA tubes, with evident TWSME observed. The typical loading conditions to trigger simultaneous transformation and plastic yield were designed, with experiments and simulations performed. According to the results, the SMA constitutive model is effective in capturing the thermomechanical response of SMA structures under various loading conditions.