Application of the Nelder-Mead method to optimize the selecting of the Likhachev-Volkov model constants

A new method was proposed for selecting constants of the modified Likhachev - Volkov microstructural model to describe the reversible strain variation during isothermal martensitic transformation in $Ti_{49}Ni_{51}$ alloy. The experimental data were approximated by solving the optimization problem using the Nelder - Mead method. A set of model parameters was found that provided the best approximation. Using the selected constants set, model qualitatively and quantitatively describe the strain variation during cooling and heating of the model sample, as well as during isothermal holding under constant stress. The proposed method of selecting constants allowed performing the smallest number of numerical experiments without requiring additional real experiments.