Large Deformation Dynamic Three-Dimensional Coupled Finite Element Analysis of Soft Biological Tissues Treated as Biphasic Porous Media

Abstract

The paper presents three-dimensional, large deformation, coupled fi- nite element analysis (FEA) of dynamic loading on soft biological tissues treated as biphasic (solid-fluid) porous media. An overview is presented of the biphasic solid- fluid mixture theory at finite strain, including inertia terms. The solid skeleton is modeled as an isotropic, compressible, hyperelastic material. FEA simulations in- clude: (1) compressive uniaxial strain loading on a column of lung parenchyma with either pore air or water fluid, (2) out-of-plane pressure loading on a thin slab of lung parenchyma with either pore air or water fluid, and (3) pressure loading on a 1/8th symmetry vertebral disc (nucleus and annulus) with pore water. For the simulations, mixed formulation Q27P8 and stabilized Q8P8 finite elements are compared (Q indicates the number of solid skeleton displacement nodes, and P the number of pore fluid pressure nodes). The FEA results demonstrate the interplay of dynamics (wave propagation through solid skeleton and pore fluid), large deformations, effective stress and pore fluid pressure coupling, compressibil- ity and viscosity of pore fluid, and three-dimensional effects for soft biological tissues treated as biphasic porous media.