Analysis of an Artery Using the ADINA Orthotropic Rubber Model
The new orthotropic rubber model of ADINA 8.2 can be used in the analysis of biomechanical materials. As a demonstration, we analyze the axial extension and inflation of the carotid artery of a rabbit. Our analysis is based on the paper, A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models, by Holzapfel, Gasser and Ogden, from Journal of Elasticity Vol. 61 (2000), pp. 1-48.
The artery is modeled as a circular cylinder with two layers: the media and the adventitia, as shown in the figure that accompanies the above animation. The layers are modeled separately using the ADINA Mooney-Rivlin rubber model with orthotropic effects. Each layer has two orthotropic directions as indicated in the figure. The material constants and fiber angles for each of the model layers are different. Note also that the orthotropic directions are not perpendicular.
To model a possible in vivo stress state, we consider the geometry of the undeformed finite element model to be an open sector of the cylinder. This is the assumed stress-free configuration of the artery.
Then the analysis is performed in three parts: closing, extension and inflation, to obtain the in vivo stressed configuration, as explained in more detail below.
Closing: The open sector of the cylinder is closed to obtain the load-free configuration of the artery. There are significant residual stresses in the load-free configuration of the cylinder.
Extension: The cylinder is then stretched in the axial direction, to simulate the physiological extension of the artery in vivo. The extension is modeled by prescribing the axial displacements of the cylinder.
Inflation: Following the extension, the cylinder is inflated by an internal pressure, to simulate the physiological pressure of the blood in vivo. The internal pressure is modeled by a deformation-dependent prescribed pressure loading.
The internal pressure/internal radius curve associated with inflation is shown in the diagram below as the green curve. As seen, the ADINA results are in agreement with the results published in the above-referenced paper.
Also shown in this diagram is the internal pressure/internal radius curve corresponding to a Mooney-Rivlin model without orthotropic effects (the red curve). Evidently the orthotropic effects are extremely important in this kind of analysis.
The Mooney-Rivlin model with orthotropic effects is obviously also very useful for many other analyses, in particular for simulations of fiber-reinforced rubber products such as tires, belts, and tubes.