Out-of-plane shear of fiber composites at moderate stretch levels

The response of incompressible fiber composites to moderate levels of out-of-plane shear and tension along the fibers is examined. It is assumed that the phases' constitutive behaviors depend on the first invariant of the right Cauchy-Green deformation tensor, and in the vicinity of the reference configuration can be approximated by a two-terms Taylor series in this invariant. A deformation field satisfying an appropriate boundary conditions on a representative cylindrical composite element is proposed, and the resulting equilibrium equations are expanded in terms of a series. A solution, which is exact to second order in the deformation, is determined. This solution provides accurate estimates for the local fields developing in a cylindrical composite with Gent phases up to one third of the locking stretch ratio. The overall response predicted by this approximated quadratic solution is found to be in agreement with corresponding results for fiber composites with Gent phases that were determined by application of a new variational procedure and by finite-element simulation of a periodic composite.