Mathematical model of intense deformed state of two-layered elastic spherical body within the porosity structure of the material

Mathematical model describing intense deformed state of two-layered heterogeneous spherical body under uniformly compressing loads within the porosity structure of the inner layer is built. Deformation of the porous medium under the influence of given uniformly compressing loads can be divided into two interrelated phases: deformation of the porous medium and further deformation of compressed matrix. Construction of mathematical model describing stress fields and displacement of the spherical body is carried out in a framework of axially symmetric installation. We have discovered analytical relations, defining the fields of stresses, strains and displacements. We have also discovered the equation for determining the deformed interface between the porous and non-porous areas for the first phase of deformation. Dependence of the external compressive loads that make initial porosity of the material reach its zero value at the whole level has been defined. We have derived analytical form for finding deflected modes in each layer during phase two. We have also deduced an equation for determining strained interface between the porous and nonporous zones. The continuity conditions of the radial component of the stress and displacement at the interface were chosen as the compatibility conditions for the strained interface of the porous and nonporous zones. We have estimated impact of each layer’s constant strength on the value of medium’s interfacial area. The curves are constructed for every of the stress components displaying the dependence of the coordinates and deformed interface of porous and nonporous zones on the parameter of initial pores’ solution within different values of physical-mechanical and geometric parameters of the material and construction.