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Abstract: It is proposed to divide the process of accumulation of irreversible deformations by a deformable solid into successive parts differing in the mechanisms of production of such deformations. With the growth of stresses in the solid due to mechanical action on it, initially irreversible deformations are produced due to the viscous properties of the material of the deformed solid as a creep deformation, and, when the stressed states emerge onto the loading surface, the mechanism of their production changes to plastic. Under unloading, the sequence reverses from a rapid plastic to a slow viscous mechanism. The continuity in such a growth of irreversible deformations is provided by the corresponding set of creep and plasticity potentials. The features of this approach are illustrated by the solution of the boundary-value problem of elastoplastic deformation on the compression of the spherical layer by an external uniform pressure, when the viscous properties of the material are specified using the Norton creep power law and the properties of the ideal plastic—by the plastic potential in the form of the Mises plasticity condition. [ABSTRACT FROM AUTHOR]

The article reports on analytical solutions for the case of viscoplastic flows of a Shvedov Bingham material, taking into consideration the elastic properties of the material. The material is treated as incompressible, and its viscosity is manifested only in the course of the plastic flow. Both the stress and strain distributions, as well as the initial moment, are determined by the properties of the material. Applying boundary conditions at equilibrium, the solution to the problem is found out mathematically.