A time integration algorithm for a 3D constitutive model for SMAs including permanent inelasticity and degradation effects

Components based on shape-memory alloys are often subjected to several loading cycles that result in substantial alteration of material behavior. In such a framework, accurate models, as well as robust and efficient numerical approaches, become essential to allow for the simulation of complex devices. The present paper focuses on the numerical simulation of quasi-static problems involving shape-memory alloy structures or components subjected to multiple loading-unloading cycles. A novel state-update procedure for a three-dimensional phenomenological model able to describe the saturation of permanent inelasticity, including degradation effects, is proposed here. The algorithm, being of the predictor-corrector type and relying on an incremental energy minimization approach, is based on elastic checks, closed-form solutions of polynomial equations, and nonlinear scalar equations solved through a combination of Newton-Raphson and bisection methods. This allows for an easy implementation of model equations and to avoid the use of regularization parameters for the treatment of nonsmooth functions. Numerical results assess the good performances of the proposed approach in predicting both pseudoelastic and shape-memory material behavior under cyclic loading as well as algorithm robustness.