Post-bifurcation of inflated fibrous cylindrical membranes under different fiber configurations

Abstract

We consider a cylindrical membrane that consists of an isotropic ground substance and fibers symmetrically arranged in two helically distributed families which are mechanically equivalent. Pressurized and axially stretched cylinders will undergo a stable inflation period that may be followed, for example, by the initiation of bulging. The pressure and deformation associated with bulging and post-bifurcation depend on various factors such as geometry and material characteristics. While the initiation of bulging has been well-studied, the post-bifurcation process has received less attention. In the post-bifurcation period, the bulge may propagate axially nucleating new configurations in equilibrium as the pressure of inflation increases. This article studies the effect of the material properties, fiber pre-stretch, fiber dispersion, and loading on both the initiation and post-bifurcation behavior of the cylinder. The results show that fiber pre-stretch may stabilize the material against bulging, whereas fiber dispersion may result in the opposite effect. A large axial stretch of the cylinder and a high fiber stiffness may result in a switch from bulging to necking in the post-bifurcation behavior.