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Thread: Porosity impact in poroelastic modeling

  1. #1
    Join Date
    Mar 2015
    Location
    Brest, France
    Posts
    48

    Default Porosity impact in poroelastic modeling

    Dear Febio community,
    It's been a year now that I am using febio for analysis on poroelastic models of the prostate. There are not sufficient data documented for the porous mechanical parameters of this tissue and I will like to do a sensitivity analysis to see how these parameters affect the model. I am interested in the volume changes and deformation field of the model during swelling phenomena. I realised for highly different values of porosity the model has the same response in terms of volume changes. This doesn't seem to be logical. Is it possibly an error induced by the coarseness of the mesh or it can be explained in other sense?

    Thank you in advance,
    Konstantinos.

  2. #2
    Join Date
    Dec 2007
    Posts
    652

    Default

    Hi Konstantinos,

    The governing equations for porous media (momentum equations and mass balance equations) are independent of the porosity. The porosity may only enter into the formulation of constitutive relations, though this is optional. In a biphasic material, there are two types of constitutive relations: (1) The stress-strain response and (2) the permeability-strain response of the porous deformable solid matrix.

    Though it is possible to formulate stress-strain responses that depend on porosity, very few of the constitutive models currently available in FEBio use an explicit dependence on the porosity. That's because the porosity in a non-reacting mixture only depends on strain (based on the mass balance equation for the porous solid matrix); therefore, a nonlinear stress-strain response can readily account for changes in porosity with deformation. In a reacting mixture, the porosity may evolve over time, in which case it would make sense to formulate a constitutive relation that depends on porosity. This is the case for the Carter-Hayes model (though the details of how that's done are a bit more elaborate than I care to describe here).

    The permeability-strain response is often modeled to depend explicitly on the porosity. Several of the permeability constitutive models in FEBio require the explicit specification of the porosity (e.g., perm-Holmes-Mow). However, the most commonly used constitutive model (perm-iso-const) does not depend on porosity. If you are using a porosity-independent constitutive model for permeability, you will not see any effect of varying the porosity on the response. In that case, your observation would be consistent with expectation. Switch to a porosity-dependent model if you would like to examine the sensitivity of the response to variations in phi0.

    Best,

    Gerard

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