Swelling and axial propagation of bulging with application to aneurysm propagation in arteries

The effect of swelling on axial propagation of bulging is investigated for thin cylinders made of doubly fiber reinforced incompressible non-linearly elastic materials. The swellable tubes are exposed to both internal pressure and axial loading. The materials under consideration are Treloar models augmented with two functions that are equal, each one of them accounting for the existence of a unidirectional reinforcement. The functions provide the anisotropic character of the material and each one is referred to as a reinforcing model. Two reinforcing models that depend only on the stretch in the fiber direction are considered: the so called standard reinforcing model and an exponential one. The former model is studied to assess the analytical methodology described in this paper. The latter one is related to soft tissue mechanical response and bulging propagation in these models establishes the connection with the propagation of aneurysms in arterial wall tissue. For the standard reinforcing model, it is shown that axial propagation of bulging is not feasible. On the other hand, for the arterial wall model axial propagation of bulging is possible for a certain range of material parameter values.