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A constitutive approach to 3-d nonlinear fluid flow through finite deformable porous continua

With application to a high-porosity polyurethane foam

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Abstract

The present paper proposes a thermodynamically consistent Forchheimer-type filter law for application in macroscopic porous media theories. The constitutive flow equation is thereby capable of describing the essential nonlinearities during 3-d fluid percolation through deformable porous solids. In particular, tortuosity effects, anisotropic properties, and the indispensable influence of finite distortions of the interconnected pore space are accounted for. However, the common shape of a Darcy-type relation is retained by assigning all nonlinearities to a general permeability tensor. Finally, to show the validity and applicability of the proposed formulation, the filter law is correlated with the data of permeability experiments on a high-porosity polyurethane foam and is used in a 3-d finite element analysis to simulate the pneumatic damping properties of the material.

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  1. Institute of Applied Mechanics (CE), University of Stuttgart, Stuttgart, Germany

    Bernd Markert

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Markert, B. A constitutive approach to 3-d nonlinear fluid flow through finite deformable porous continua. Transp Porous Med 70, 427–450 (2007). https://doi.org/10.1007/s11242-007-9107-6

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