One-dimensional constitutive behavior of shape memory alloys: Thermomechanical derivation with non-constant material functions and redefined martensite internal variable

A one-dimensional constitutive model for the thermomechanical behavior of shape memory alloys is developed based on previous work by Liang and Tanaka. An internal variable approach is used to derive a comprehensive constitutive law for shape memory alloy materials from first principles without the assumption of constant material functions. This constitutive law is of such a form that it is well suited to further practical engineering applications and calculations. A separation of the martensite fraction internal variable into temperature-induced and stress-induced parts is presented and justified, which then allows the derived constitutive law to accurately represent both the pseudoelastic and shape memory effects at all temperatures. Several numerical examples are given that illustrate the ability of the constitutive law to capture the unique thermomechanical behavior of shape memory alloys due to their internal phase transformations with stress and temperature.