Distribution of stress and displacement fields in a porous spherical body with allowance for elastic and plastic properties

A mathematical model of the intense deformed state of a spherical body under hydrostatic compression has been constructed. A porous continuum the squeezed skeleton of which possesses strengthened elasto-plastic properties was chosen as the material model. Deformation of the porous environment under the action of uniformly distributed squeezing loads is divided into two stages: elastic deformation of the porous environment and inelastic deformation of the squeezed matrix. At the first stage, only the deformation caused by partial external pressure and leading to complete compression of the initial porosity in the whole body is considered. The resulting solution of the first tasks of the intense deformed state is taken as the initial state for the second phase in which the remainder of the external pressure is applied to the body. Constructing a mathematical model describing the stress field and displacement field for a spherical body was carried out within the centrally symmetric formulation. The relations determining fields of tension and displacements at the first stage of deformation have been found. The squeezing pressure under which the initial porosity of material in the entire body reaches the zero value has been determined. At the second stage of the deformation process, analytical expressions for fields of tension and displacements in elastic and plastic deformation zones of the squeezed skeleton are derived, and the equation for determining the radius of the elasto-plastic border is obtained. The effect of hardening and fluidity limits on the size of the border area between elastic and plastic deformations of the initial porosity is estimated.