Poroelasticity of saturated solids with an application to blood perfusion

A description of finite deformation of, and fluid flow through, a hierarchically arranged porous solid has been developed using the theory of mixtures. This hierarchical mixture consists of one solid constituent and a fluid constituent that is subdivided into a continuous series of intercommunicating compartments. Conservation laws for mass and momentum have been derived and appropriate formulations for the constitutive behaviour of the constituents are proposed. A finite element description of the hierarchical mixture model has been implemented in the software package DIANA. Two-dimensional, axisymmetric and three-dimensional elements can be used in finite deformation analysis. An example of application is blood perfused biological tissue. A simulation of a blood perfused contracting skeletal muscle is presented.

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