A FINITE-ELEMENT MIXTURE MODEL FOR HIERARCHICAL POROUS-MEDIA

A finite element description of fluid flow through a deforming porous solid, with a hierarchical structure of pores, has been developed and implemented in the finite element software package DIANA.(1) Several s tandard element types can be used for 2-D, axisymmetric and 3-D finite deformation analysis, The hierarchy is dealt with as an extra dimensi on, quantified by a parameter x(0). Both spatial and hierarchical flui d flow is described by a Darcy equation. Fluid pressure and hydrostati c solid pressure are related via an elastic fluid-solid interface. The state of the fluid, the Darcy permeability tensor and the elastic int erface depend on both spatial position and hierarchical level. Discret ization and integration of fluid related quantities are split into a s patial and a hierarchical part. The degrees of freedom of the finite e lement model are the displacements of the solid, the hydrostatic press ure and a number of fluid pressures on different hierarchical levels. Blood-perfused biological tissue can be regarded as a hierarchical por ous solid, where the fluid represents the blood and the hierarchy corr esponds to the tree-like vascular structure. As an example, a simulati on of a contracting, blood-perfused skeletal muscle is presented.