Filtration in fluid-saturated poro-plastic materials during lateral extrusion

It is known that non-compact materials (porous, powdery, with defects in continuity) are much less resistant to shear than to hydrostatic compression. The effect of dilatancy in such media causes a change in density during shear deformation. For compact materials, a process of lateral extrusion (or equal-channel angular pressing) is known. The ECAP realizes a stress state close to a pure shear in the deformation zone (as opposed, for example, to direct extrusion, where a simple shear is realized). It can be expected that ECAP process for non-compact materials is less energy consuming and leads to a more intensive consolidation of the frame material than hydrostatic compression. In particular, ECAP can be considered as one of the methods of extracting the fluid from a porous medium (oils from vegetable raw materials, water from soils, etc.). This paper is devoted to modeling of such processes. We consider the plane problem of stationary plastic deforming of a material in the region of junction of slot channels. The cross section of the deformation region is an annular sector. We assume that the material is irreversibly compressible and obeys the elliptic Green type yield condition. One of the walls of the channel is permeable to fluid. We consider the fluid filtration in the pores. We use a number of model assumptions. The motion of the frame material particles is a flat azimuthal in a cylindrical coordinate system. The mechanical characteristics of the material vary slightly in accordance with small changes in density. The intraporous pressure is small in compare with the stressed state of the skeleton material and does not have a significant effect on the process of plastic flow. A rigid-plastic analysis was performed and the exact solution of the mechanical part of the problem was obtained. The exact solution of the fluid filtration problem in case of a constant filtration coefficient is obtained. The solution is the intraporous pressure field. When using these results one can determine the two-dimensional vector field of the fluid velocity and the total discharge of flow. In case of a non-constant filtration coefficient, the problem is reduced to integrating the boundary value problem of anisotropic thermal conductivity with a special case of anisotropy, for which a number of exact solutions are known.