A Generalized Maxwell Model for Creep Behavior of Artery Opening Angle

An artery ring springs open into a sector after a radial cut. The opening angle characterizes the residual strain in the unloaded state, which is fundamental in understanding stress and strain in the vessel wall. A recent study revealed that the opening angle decreases with time if the artery is cut from the loaded state, while it increases if the cut is made from the no-load state due to viscoelasticity. In both cases, the opening angle approaches the same value in $3h$⁠. This implies that the characteristic relaxation time is about $10,000s$⁠. Here, the creep function of a generalized Maxwell model (a spring in series with six Voigt bodies) is used to predict the temporal change of opening angle in multiple time scales. It is demonstrated that the theoretical model captures the salient features of the experimental results. The proposed creep function may be extended to study the viscoelastic response of blood vessels under various loading conditions.