Dynamic Finite Strain Biphasic Poromechanics of a 'thin' Poroelastic Layer

Abstract

In biological tissues, there are many thin, deformable, porous materials, such as basement membranes like the ocular lens capsule [Kaufman and Alm, 2003, Candiello et al., 2007] that, when subjected to dynamic loading, can exhibit coupling between solid skeleton deformation and relative pore fluid flow. These materials deform at finite strain and, since they are thin, they can be modeled as solid-shells [Tan and Vu-Quoc, 2005]. We are in the process of developing a finite strain, dynamic, poromechanical solid-shell finite element. But to start, we first present the results of applying a three-dimensional, Total Lagrangian, finite strain, dynamic, biphasic mixture finite element implementation [Regueiro and Ebrahimi, 2010] to simulate the dynamics of a `thin' poroelastic layer of lung tissue (for which we have porosity, permeability, and elastic parameter estimates from the literature [Lande and Mitzner, 2006, Levental et al., 2006]). The results will demonstrate the importance of accounting for the dynamics of solid skeleton deformation and relative fluid flow in `thin' poroelastic layers, where estimates of effective stress that the solid skeleton experiences are important in developing dynamic failure models of thin, deformable, porous materials.