The evolution of regions of reversible and irreversible deformation within a hollow sphere with complex rheological properties under conditions of unsteady heating

The Ivlev–Sporykhin continuum model, which is a model of a hardening elastoviscoplastic solid, is considered in this study. The model takes into account both reversible and irreversible deformations to investigate evolutionary processes occurring in a hollow sphere under the influence of a time-dependent temperature field. During the solution of this problem, an analytical expression for the temperature distribution within the body was derived. A generalized tree of evolution of regions of elasticity, plastic flow, unloading, and re-plasticity was also constructed. Expressions for the radial components of stress and displacement in these regions were also developed. Four rheological models were compared, taking into account the various properties of the medium.