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Double porosity in fluid-saturated elastic media: deriving effective parameters by hierarchical homogenization of static problem

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Abstract

We propose a model of complex poroelastic media with periodic or locally periodic structures observed at microscopic and mesoscopic scales. Using a two-level homogenization procedure, we derive a model coherent with the Biot continuum, describing effective properties of such a hierarchically structured poroelastic medium. The effective material coefficients can be computed using characteristic responses of the micro- and mesostructures which are solutions of local problems imposed in representative volume elements describing the poroelastic medium at the two levels of heterogeneity. In the paper, we discus various combinations of the interface between the micro- and mesoscopic porosities, influence of the fluid compressibility, or solid incompressibility. Gradient of porosity is accounted for when dealing with locally periodic structures. Derived formulae for computing the poroelastic material coefficients characterize not only the steady-state responses with static fluid, but are relevant also for quasistatic problems. The model is applicable in geology, or in tissue biomechanics, in particular for modeling canalicular-lacunar porosity of bone which can be characterized at several levels.

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Authors and Affiliations

  1. NTIS New Technologies for Information Society, European Centre of Excellence, Faculty of Applied Sciences, University of West Bohemia in Pilsen, Univerzitní 22, 30614, Plzeň, Czech Republic

    Eduard Rohan

  2. Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, Université Paris-Est, 61, Avenue du Général de Gaulle, 94010, Créteil Cedex, France

    Salah Naili & Thibault Lemaire

Authors
  1. Eduard Rohan
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  2. Salah Naili
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  3. Thibault Lemaire
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Correspondence to Salah Naili.

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Communicated by Andreas Öchsner.

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Rohan, E., Naili, S. & Lemaire, T. Double porosity in fluid-saturated elastic media: deriving effective parameters by hierarchical homogenization of static problem. Continuum Mech. Thermodyn. 28, 1263–1293 (2016). https://doi.org/10.1007/s00161-015-0475-9

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