Porohyperelastic theory and finite element models for soft tissues with application to arterial mechanics

Abstract

Biological structures composed of soft tissues can be studied. using poroelastic models, i.e., the material is viewed as a highly deformable porous solid skeleton that is saturated by mobile tissue fluid. These structures exhibit nonlinear material behavior and undergo finite strains. A ‘porohyperelastic’ (PHE) field theory is presented as a natural extension of classical hyperelasticity. Eulerian and Lagrangian forms for the field equations are given for materials in which both the solid skeleton and the fluid are incompressible. These forms allow proper identification of two fundamental material property functions, the effective strain energy density function and the hydraulic permeability. Eulerian and Lagrangian mixed finite element models (FEMs) are presented that include the PHE material response and finite strains. Applications of PHE theory and FEMs developed using the ABAQUS program are described for the study of large arteries. Representative functional forms for the material properties are given that include the necessary material constants in the strain energy density function and the hydraulic permeability. Both steady-state and transient cyclic pressurization of a large artery are simulated using ABAQUS FEMs of an axisymmetric segment of a PHE tube constrained in finite plane strain.