Bifurcation of Fiber-Reinforced Cylindrical Membranes under ‎Extension, Inflation, and Swelling

Abstract

We analyze bifurcation for a cylindrical membrane capable of swelling subjected to combined axial loading and internal pressure. The material is conceptualized as an isotropic and absorbent matrix (it can swell when it is exposed to some swelling agent, for instance) containing nonabsorbing fibers. More in particular, fibers are symmetrically arranged in two helically distributed families which are (also) mechanically equivalent. Arterial wall tissue has been modeled using this theoretical framework. The matrix of the membrane is taken to be a swellable neo-Hookean material. The swollen membrane is then inflated and axially stretched so that the circular cylindrical geometry is initially preserved. Nevertheless, prismatic, bulging, and bending (composite) bifurcation conditions are analyzed. It is shown that for membranes with and without fibers, prismatic bifurcation does not play a major role. On the other hand, bending and bulging are feasible for fiber-reinforced membranes. Results capture the onset of bifurcation configurations corresponding to bending and bulging and highlight possible coupling during postbifurcation as it might occur, for example, in the formation and development of an abdominal aortic aneurysm.

Keywords

• bulging bifurcation
• bending bifurcation
• prismatic bifurcation
• swelling
• fibers
• hyperelasticity