Determination of the mechanical properties of the porcine thoracic aorta and an analysis of the stress concentration in fiber reinforced nonlinear solids

Abstract

Knowledge of the mechanical properties of the thoracic aorta and determining appropriate constitutive relations are essential in developing computational methodologies for the accurate prognosis of vascular diseases like aortic aneurysm and dissection. We study tearing and uniaxial properties of the porcine thoracic aorta, and investigate the influence of certain constitutive assumptions on the local stress distribution around a circular hole in two-fiber reinforced materials.

We performed peeling experiments on the ascending and the descending segments of the porcine thoracic aorta to evaluate its tearing characteristics. The stretch experienced by the peeled halves, peel force per unit width and peeling energy per unit area reveal segment-specific differences in the tearing characteristics of the porcine thoracic aorta. Further, the influence of non-linear mechanical response of the aorta on the estimation of the peeling energy per unit area is investigated.

Using uniaxial extension tests, we examine the directional variation of the mechanical properties of the porcine thoracic aorta. Dumbbell-shaped samples are cut from the aortic wall at five different orientations with respect to the circumferential direction of the aorta and are subjected to cyclic uniaxial extension and extension until failure. Specimens in all the orientations considered show a nonlinear constitutive response that is typical of collagenous soft tissues. Shear strain under uniaxial extension demonstrates clearly discernible anisotropy of the mechanical response of the porcine aorta. The samples oriented at 45o and 60o with respect to the circumferential direction show a peculiar crescent-shaped shear strain-nominal stretch response. Failure stress indicates a decreasing tensile strength of the porcine aortic wall from the circumferential direction to the longitudinal direction.

The forms of the stored energy function that are commonly used for modeling arteries are dependent only on a subset of the full invariant set that is necessary to model two-fiber reinforced materials. We study the influence of such assumptions on the deformation and the stress distribution around a small circular hole in a thin nonlinearly elastic large sheet reinforced by two families of fibers undergoing large deformations. Results indicate a strong influence of the constitutive assumptions on the stress concentration factors. A significant difference in the stress concentration factor distribution around the hole is observed when using a constitutive relation based on a partial set of invariants versus an "extended" constitutive relation that incorporates the full set of invariants appropriate for a body reinforced with fibers and reduces appropriately to the orthotropic linearized elastic case. We show how two constitutive relations that exhibit a similar biaxial behavior in the absence of discontinuities display noticeable differences in the presence of discontinuities like a circular hole.