On Residual Stresses in Arteries

In the study of vascular elasticity the unloaded state (one with zero transmural pressure and zero axial load) is commonly used as the reference state in which stresses and strains are considered as zero everywhere. Strains at loaded states are defined with respect to this state. Stress-strain relationships are identified under the assumption that the vessel wall is stress-free at this unloaded state. Evidence of the existence of residual stresses in the arterial wall at the unloaded state is given in Fung [4]. With a longitudinal cut along the vessel wall the unloaded specimen springs open and its cross section becomes a sector. The opening angle of the vessel wall is time-dependent after the sudden relief of the initial residual stress. It shows that the artery is not stress-free at the unloaded state. It is important to identify the stress-free state. When we use pseudoelasticity [3] to characterize the arterial wall, we need a stress-free state as the reference state for strain measurements. Correspondingly, we also want to define stress with respect to this same reference state so that we can relate stresses to strains easily. Presence of the residual stress at the unloaded tube state will certainly affect the evaluation of stress distribution in the arterial wall due to actual loadings in the physiological range. In this note we present a method to describe the geometry of the opened-up stress-free state of the artery, which is taken to be the reference state. An algorithm is outlined for the identification of the stress-strain relationship of the arterial wall. Residual stresses, and strains in the unloaded tube are evaluated. With the consideration of residual stresses the stress distributions due to loadings in the physiological range are also evaluated.