INHOMOGENEOUS STRESS-DEFORMED STATE OF AN ELASTIC CYLINDRICAL BODY TAKING INTO ACCOUNT ITS MATERIAL INTERNAL STRUCTURE

Objectives. An investigation of the stress-deformed state of a poroelastic cylindrical body under uniform radial compression.

Methods. Mathematical modeling based on the phenomenological approach for the description of porous media, as well as within the framework of geometrically linear relations of the theory of elasticity.

Results. A mathematical model is constructed to describe the inhomogeneous stress-deformed state of a cylindrical body for materials having a porous structure under elastic operation of a fully compressed matrix. The deformation of the porous medium under uniformly distributed compressive loads is divided into two interrelated stages: the elastic deformation of the porous compressible medium and the elastic deformation of a fully compressed matrix for which further incompressibility is a defining property. The problem of determining the stress-deformed state of a cylindrical body at each stage of deformation is solved within the framework of a planar deformation. This does not take into account effects associated with the fact that the cylindrical body under consideretion has a finite height. Relations determining the stress and displacement fields at each stage of deformation are obtained. The dependency of external loads is determined for which the initial porosity of the material reaches zero throughout the entire body. The graphical dependencies of the stress components on the coordinate are constructed for the different values of initial pore solution and other physical-mechanical and other material and structural geometric parameters.

Conclusion. The constructed analytical dependencies describe the inhomogenous distribution of stress and displacement fields at the deformation stage of materials having a porous structure and a cylindrical body with a fully compressed matrix. These relations are consistent with the general physical concepts of the processes under consideration and allow for a limiting transition to known solutions.

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