Nonlinear Anisotropic Elastic Properties of the Canine Aorta

Abstract

A nonlinear theory of large elastic deformations of the aortic tissue has been developed. The wall tissue has been considered to be incompressible and curvilinearly orthotropic. The strain energy density function for the tissue is expressed as a polynomial in the circumferential and longitudinal Green-St. Venant strains. Limiting application to states of strains wherein the geometric axes are the principal axes and truncating the energy expression to include terms with highest degrees 2, 3, and 4, three expressions with 3, 7, and 12 constitutive constants are obtained. Results of application of these expressions to data from three series of in vitro and in vivo experiments involving 31 dogs have been presented. Whereas all the three expressions are found to be applicable to various degrees, the third-degree expression for the strain energy density function with seven constitutive constants is particularly recommended for general use.