This study proposes a mathematical model to investigate stability of arteries. The artery is considered as a prestressed thick-walled tube subjected to dynamical pressure and made of a hyperelastic and composite material [1]. To model the mechanical contributions of the different arterial components, the here considered constitutive law of the wall takes into account the isotropic part due to the elastin-dominated matrix and the anisotropic due to the collagen fibers [2]. In this context, the purpose of this work focuses on the initial formation of aneurysms in human arteries which may be modelled as instability phenomena. For that, a perturbation technique is used on the equations of motion to highlight possible instabilities of the artery. This instability interpretation provides a theoretical approach under which different biological mechanisms leading to the risk of aneurysm formation can be assessed.

The proposed approach shows the influence of disturbances on the time variation of the radial deformation at the inner surface of the arterial wall. This means that the stress distributions are very sensitive to disturbances and may explain the aneurysm formation and its growth.