An axisymmetric steady-state flow through a poroelastic medium under large deformations

We present an example of the solution of a boundary value problem for a two-component porous material with large deformations of the skeleton. This example demonstrates the application of a consistent Lagrangian description of porous materials which has been proposed by K. Wilmanski. Simultaneously we demonstrate the important role of the balance equation of porosity which is an essential part of the thermodynamical model of porous materials proposed by K. Wilmanski. We show as well that a modified set of boundary conditions for permeable boundaries yields a solution of field equations which agrees qualitatively with expectations for the problem of axisymmetric stationary filtration. On the basis of a numerical evaluation of solution we indicate the existence of an instability of the model for very large porosities which could not be explained in this work