Computational modelling of bulging of inflated cylindrical shells applicable to aneurysm formation and propagation in arterial wall tissue

In this paper we use a numerical procedure to analyse bifurcation and postbifurcation of inflated hyperelastic thick-walled cylinders based on the modified Riks method. In particular, the bulging mode of bifurcation is exploited in the context of aneurysm formation with cylindrical geometry in cardiovascular diseases. We focus here on orthotropic materials with two preferred directions which are mechanically equivalent and are symmetrically disposed. Arterial wall tissue is modeled with this class of constitutive equation showing significant stiffening behaviour. The onset of bulging is considered to give aneurysm formation. Analytical solutions can be found in the literature for very particular conditions involving specific material models and loads applied as well as, usually, a perfect geometry. Here, we provide a unified approach to both the prediction of bifurcation and postbifurcation propagation that can be applied to more general conditions. Furthermore, we show that bulging instability under the conditions at hand propagates axially in agreement with the propagation of aneurysms in arterial wall tissue.