Mathematical model of the stress-strain state of an elastic cylindrical body with a porous filler

The mathematical model of intense deformed state of two-layer cylindrical body under uniform compressive loads considering the porous structure of inner layer was defined. Building a mathematical model describing the stress field and displacement field for a cylindrical body was carried out considering a plane strain. Deformation of the porous environment caused by evenly distributed squeezing pressure is divided into two stages: deformation of the porous environment and deformation of the squeezed matrix.In the first stage the material model was assumed compressible elastic body model, the second — the model of elastic incompressible medium. As a full compression condition at a certain point of the medium at this point was assumed equality volumetric strain a given value — the initial pore size, characterizing the pore volume of the sample in the non-deformed state. Squeezing pressure, under which the initial porosity of material in the whole layer reaches zero value, is defined. At the first and second stage of the deformation process, the analytical expressions of fields of tension, strain and displacements in the inner and external layer are defined. As the compatibility conditions at the interface between layers selected terms the continuity of the radial component of the stress and displacements. Consider the nature of influence of the elastic constants of the material both internal and external layer on the distribution of the stress field.