Methods of Nonlinear Dynamics of Nonequilibrium Phase Transitions in the Theory of Failure of Materials

The article attempts to extend the methodology of mathematical modeling of critical phenomena as nonequilibrium phase transitions occurring at the initial stages in the spinodal decomposition mode to the process of destruction of structural materials. The method of thermodynamic analysis of critical phenomena is considered using the example of constructing a mathematical model of transformation from elastic deformation to creep. A mathematical description is given of elastic deformation, plastic flow, and irreversible transition of one into another in a single-phase model, without isolating the transformed state as an independent phase; formation of a creep zone in the terminology of Barenblatt.