Stochastic superelastic properties of materials with phase transformations

The study is devoted to the impact of stochastic isothermal phase transformations in an unstable material on its superelastic hardening.
A stochastic differential equation is derived to describe the dynamics of nucleation, growth of the new phase volume, and its interaction with the parent phase, depending on the level of irreversible structural deformations.
Macroscopic constitutive relations are established for the unstable material, incorporating the stochastic nature of phase transformations and their dependence on structural deformations. Effective elastic moduli of the material are calculated based on these relations.
Stochastic differential equations for direct and reverse phase transitions are formulated.
Numerical simulations demonstrate strong agreement with experimental data, validating the proposed model.