Swelling-twist interaction in fiber-reinforced hyperelastic materials: the example of azimuthal shear

We study how fiber-reinforced materials will naturally undergo swelling deformations in which a relatively greater stretch occurs transverse to the fibers than in the fiber direction. This means that a pattern of initially curved fibers prior to swelling will tend to straighten out as swelling proceeds. This can lead to swelling-induced deformations with a high degree of localized shearing and significant overall twisting. Such a process is examined for a plane strain swelling deformation that combines twist with radial expansion. Analytical results are obtained for both types: small and large swelling. Of particular interest is the relation of the extensible fiber theory to a theory for inextensible fibers. We examine the extent to which the former approaches the latter in the limit as the fibers are taken to be progressively stiffer.