  The response of a neo-Hookean fiber composite undergoing finite out-of-plane
shear deformation is examined. To this end an explicit close form solution for
the out-of-plane shear response of a cylindrical composite element is
introduced. We find that the overall response of the cylindrical composite
element can be characterized by a fictitious homogeneous neo-Hookean material.
Accordingly, this macroscopic response is identical to the response of a
composite cylinder assemblage. The expression for the effective shear modulus
of the composite cylinder assemblage is identical to the corresponding
expression in the limit of small deformation elasticity, and hence also to the
expression for the Hashin-Shtrikman bounds on the out-of-plane shear modulus.
