In this article, we study the inflation and bulging of fiber reinforced hyperelastic membranes in which fibers are symmetrically arranged in two helically distributed families that are mechanically equivalent. The isotropic ground substance behavior is described by a neo-Hookean model and the mechanical behavior of fibers is described by the so-called standard reinforcing model. The two constituents, fiber and matrix, may possess different natural configurations to account for different characteristics. For example, in collagenous soft tissue synthesized collagen fibrils are integrated at a certain distribution of pre-stretches, or fibers may be crimped, and different natural configurations of the constituents can be used to model these mechanisms. In addition, fibers are taken to be dispersed with respect to a mean fiber direction within their respective fiber families. It is shown that the arrangement and the natural configuration of fibers have a strong effect on bulging of inflated cylindrical membranes. The modeling at hand can be used to understand the mechanical behaviour of arterial soft tissue and the formation of aneurysms.
Read full abstract