Validity Analysis of Elastic-Plastic Deformation Mechanics Problems Considering the Growth of Pores in the Material Via the Rice–Tracey–Huang Models. Part 3. Generalized Rice–Tracy–Huang Equation.

The validity conditions of nonlinear problems of mechanics of elastic-plastic deformation, which take into account the evolution of the growth of the volume of nucleated pores in the material based on the generalized Rice–Tracey–Huang equation, are investigated. This equation combines the classical Rice–Tracey–Huang equations, in which an additional continuous function greater than zero is introduced, which depends on the stiffness of the stress state and has a nonnegative derivative. With this modification of the classical Huang equation, the properties of the governing equations for the analysis of the porosity of irradiated material are improved, which contributes to the weakening of the restrictions on the initial data associated with the stiffness of the stress state. Using the generalized Rice–Tracey–Huang equation, the governing equations of material behavior are formulated to describe the nonisothermal processes of elastic-plastic deformation, taking into account the increase in the concentration of ductile fracture pores in the material. The loading process is divided into separate calculation stages, and for each of them, the plastic flow equation and the generalized Rice–Tracey–Huang equation are integrated for the loading stage. Due to integration, the governing equations for the full stress and strain components are obtained, which allows us to describe the processes of active loading, unloading, and reloading. Irreversible deformations in these equations include accumulated plastic deformations and structural volumetric deformations that take into account the concentration of pores in the material. The conditions are formulated under which the dissipation power and the power developed by the additional stresses on the additional deformations caused by them do not decrease in the process of loading the porous material. On the basis of the obtained energy inequalities, which generalize the postulate of Drucker's strengthening in relation to the porous material, the conditions are established that ensure the correctness of the formulated plasticity equations, which take into account the growth of pore concentration in the material on the basis of the generalized Rice–Tracey–Huang equation. [ABSTRACT FROM AUTHOR]