A new derivation of the bifurcation conditions of inflated cylindrical membranes of elastic material under axial loading. Application to aneurysm formation

We provide a simple proof of the bifurcation criteria for a membrane cylinder subjected to combined axial loading and internal pressure. Three modes of bifurcation are discussed: a prismatic mode, a bulging mode and a composite mode. The bulging mode of bifurcation is further exploited in the context of aneurysm formation with cylindrical geometry in cardiovascular diseases. In particular, the bulging mode is taken as the initiation of aneurysm formation. The role that the collagen fibers inside the arterial walls play is established. It is shown that healthy collagen fibers stabilize the artery and avoid aneurysm formation. Collagen fibers give the anisotropic character to the mechanical response of arteries. The presence of these fibers also give rise to the so called strain stiffening mechanism. We show here that loss of tissue anisotropy associated with a strain softening mechanism of the collagen fibers may play an important role in the initiation of aneurysms.