Irreversible deformation and subsequent unloading of a spherical elastoviscoplastic layer

Analytical solutions of a number of one-dimensional quasi-static problems that describe the processes of elastic deformation of the material of a hollow sphere and of generation and development of the plastic flow in this material with increasing pressure on the external boundary are presented. The process of unloading during slow removal of the loading pressure is studied. Stress fields, fields of elastic and plastic strains in the material of the spherical layer, the law of motion of the elastoplastic boundary, and residual stresses are determined. It is demonstrated that (in contrast to the ideal plasticity case) the allowance for the viscous properties of the material during its plastic flow eliminates the possibility of plastic flow emergence during unloading.