A hyperelastic constitutive model for fiber-reinforced rubber-like materials

In this paper, a Strain Energy Function (SEF) is proposed to characterize the hyperelastic behavior of transversely isotropic incompressible fiber-reinforced rubbers. The kinematics of the deformation is based on a strain measure consistent with the physics of the deformation. The SEF consists of an isotropic part and an anisotropic one where a simple form of SEF is used for both parts. In order to investigate the capabilities of the proposed model, two fiber-reinforced rubbers under homogeneous deformations are examined. The predictions of the model show a good agreement with the experimental data for both tensile and shear deformations. Also, torsion of a fiber-reinforced rubbery circular cylinder is investigated. It is shown that, in the absence of an additional axial force, the cylinder may elongate (Poynting effect) or contract (reverse-Poynting effect) based on the fibers angle and the amount of deformation.