Nonlinear structural analysis of poroelastic materials and its application in arteries.

Abstract

In this thesis, the nonlinear poroelastic theory including finite strain, material nonlinearity and material incompressibility is presented systematically in an axisymmetric cylindrical coordinate system using a total Lagrangian description. The large arteries are viewed as poroelastic materials. Special efforts are made to develop the material constitutive relations and incompressibility constraints among material properties. The material property tests and experimental data reduction schemes for poroelastic material under finite strain are discussed as a nonlinear inverse problem. The author shows that the finite strain poroelastic theory is a natural extension of conventional finite strain elastic theory. The finite element formulation is derived from poroelastic theory in full detail using Galerkin approach. The displacement formulation of the finite element method is expanded to include the displacements of pore fluid relative to the deforming solid. The penalty method and selective reduction integration are implemented for poroelastic materials composed of incompressible solid and incompressible fluid. A finite element computer code using four-node isoparametric element was programmed for both cylindrical and Cartesian coordinate systems. Examples are given to verify the computer program and demonstrate the generality of the poroelastic theory. Basic structural analyses using finite element methods are carried out and discussed.