The stress-strain state of the double-layer spherical construction taking into account the porous structure of inner layer and heterogeneity of outer layer

Abstract

The mathematical model describing the stress-strain state of a double-layer spherical body is constructed. The inner layer of the considered body has a porous structure, and the outer layer has nonhomogeneous elastic properties. Deforming of the porous medium under the specified uniformly distributed compressive loads is divided into two stages: elastic deforming of the porous medium and inelastic deforming of the compressed matrix having hardening elastic-plastic properties. The mathematical model describing the stress and displacement fields for a double-layer spherical body is constructed within the framework of the centrally symmetric formulation. The analytical relations that define the stress and displacement fields for both layers at the first stage of deforming are obtained. The analytical expressions that describe the stressstrain states in the elastic and plastic deforming zones of the inner layer with a fully compressed matrix, as well as the outer layer are found. The equation for defining the radius, which separates the elastic and plastic deforming zones of the inner layer at the second stage of deforming is obtained. The consistency conditions at the elastic-plastic boundary were chosen as follows: 1) the continuity conditions of the radial component of stresses and displacements; 2) the equality to zero of plastic deformations on the radial component of stresses and displacements. The continuity conditions of the radial component of stresses and displacements were chosen as consistency conditions on the boundary between the layers.