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Mathematical framework for unsaturated flow in the finite deformation range
Author(s) -
Song Xiaoyu,
Borja Ronaldo I.
Publication year - 2013
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4605
Subject(s) - deformation (meteorology) , porous medium , porosity , materials science , saturation (graph theory) , mechanics , mixture theory , fluid dynamics , degree of saturation , poromechanics , geotechnical engineering , mathematics , composite material , geology , physics , statistics , combinatorics , mixture model , soil science , soil water
SUMMARY The presence of fluid in the pores of a solid imposes a volume constraint on the deformation of the solid. Finite changes in the pore volume alter the degree of saturation of a porous material, impacting its fluid flow and water retention properties. This intricate interdependence between the hydromechanical properties related to solid deformation and fluid flow is amplified when the deformation of the solid matrix is large. In this paper, we present a mathematical framework for coupled solid‐deformation/fluid‐diffusion in unsaturated porous material considering geometric nonlinearity in the solid matrix. The framework relies on the continuum principle of thermodynamics to identify an effective or constitutive stress for the solid matrix, and a water‐retention law that highlights the interdependence of the degree of saturation, suction, and porosity of the material. Porous materials are typically heterogeneous, making them susceptible to localized deformation. In this work, we consider random heterogeneities in density and degree of saturation as triggers of localized deformation in a porous material. Copyright © 2013 John Wiley & Sons, Ltd.