Neo-Hookean fiber composites undergoing finite out-of-plane shear deformations

TL;DR

This paper derives an explicit solution for the out-of-plane shear response of neo-Hookean fiber composites, showing that their macroscopic behavior can be modeled by a homogeneous neo-Hookean material with bounds matching classical elasticity limits.

Contribution

It introduces a closed-form solution for finite out-of-plane shear deformation in neo-Hookean fiber composites and links the response to a homogeneous material model.

Findings

The composite's response is characterized by a fictitious homogeneous neo-Hookean material.

The effective shear modulus expression matches classical elasticity bounds.

The macroscopic response aligns with the Hashin-Shtrikman bounds.

Abstract

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.