Role of Fiber Orientations and Invariant Coupling in the Stress–Strain Non-Coaxiality of Bioinspired Fiber-Reinforced Elastomers

Abstract

Stress–strain coaxiality is a key determinant in generating universal relations for materials. These relationships have been studied extensively in isotropic materials but remain underexplored in fiber-reinforced materials with different material symmetries. The present study aims to examine the role of fiber orientations and invariant coupling in the stress–strain coaxiality of transversely isotropic fiber-reinforced elastomers (FREs) under simple shear, uniaxial tension, and nonequibiaxial stretch. The strain energy density as a function of the invariants I1 (matrix) and I4 (fiber) is adopted with nonlinear coupling exponents (α,β). Illustrations are presented on how different invariant coupling terms affect the stress–strain coaxiality-driven universal relations for the transversely isotropic material class. Variations in axial vector terms are reported for different stretches, fiber orientations, and the degree of nonlinearity in the coupling terms with their coupling exponents. Such variations are compared across three distinct deformation modes: simple shear, uniaxial tension, and nonequibiaxial stretch. In all three modes, the inclusion of the I1−I4 invariant coupling term significantly altered the stress–strain coaxiality relations for θ=45deg, 60deg, and 75deg. These results provide significant evidence of the importance of fiber–matrix coupling terms in the constitutive properties of FRE materials.