Methods for identification of material constants associated with the martensite stabilization effect in shape memory alloy models

The martensite stabilization effect significantly influences the thermomechanical response of shape memory alloys and must be properly taken into account in numerical modeling. In our previous studies, to describe this effect in TiNi alloys we developed a model using the microstructural approach. The foundation of the model was the hypothesis of damage accumulation at inter-martensitic boundaries. In this work, four approaches to the identification of material constants of this model are considered: manual fitting, the deterministic Nelder--Mead method, a stochastic genetic algorithm, and a neural network approach based on the Deep Sets architecture. The study uses the results of experiments for the Ti50Ni50 and Ti49Ni51, titanium nickelide alloys reported in the literature. These experiments reproduce three characteristic modes of applying preliminary deformation: tensile deformation in the martensitic state, cooling under constant load, and stress-induced martensite transformation. The parameter identification procedure aims to minimize the discrepancy function measuring the difference between the calculated and experimentally observed shifts in the reverse martensitic transformation temperature. A comparison of the accuracy and computational efficiency of the applied methods was carried out for both alloys. The results show that the Nelder--Mead method and the genetic algorithm provide a comparable quality of the experimental data approximation at moderate computational costs and relatively simple parameter setting. The neural network approach demonstrates less accurate agreement between the results of numerical simulation and experiments but provides fast inference after training; however, it requires pre-generation of large training datasets and exhibits increased sensitivity to the initial training conditions. The obtained results confirm the applicability of different methods of automated parameter identification for models of shape memory alloys.