Neo-Hookean fiber composites undergoing finite out-of-plane shear   deformations
  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. 
G. deBotton and I. Hariton