A Poroelastic Finite Element Formulation Including Transport and Swelling in Soft Tissue Structures

Abstract

A field theory is presented for the study of swelling in soft tissue structures that are modeled as poroelastic materials. As a first approximation, soft tissues are assumed to be linear isotropic materials undergoing infinitesimal strains. Material properties are identified that are necessary for the solution of initial boundary value problems where swelling and convection are significant. A finite element model is developed that includes the solid displacements, the relative fluid displacements, and a representative concentration as the primary unknowns. A numerical example is presented based on a triphasic model. The finite model simulates a typical experimental protocol for soft tissue testing and demonstrates the interaction and coupling associated with relative fluid motion and swelling in a deforming poroelastic materiaL The theory and finite element model provide a starting point for nonlinear porohyperelastic transport-swelling analyses of soft tissue structures that include finite strains in anisotropic materials.