Characterization of strain-induced anisotropy in isotropic hyperelastic materials via generalized incremental moduli

This paper introduces a generalized formulation of incremental elastic moduli for the characterization of strain-induced anisotropy in isotropic hyperelastic materials. The proposed approach extends the classical concept of incremental stiffness moduli, which are traditionally limited to specific deformation modes such as uniaxial stress, simple shear, or hydrostatic stress, by enabling the evaluation of tangent stiffness under arbitrary deformation states. This represents a novel and unified framework for quantifying deformation-induced anisotropy and directional stiffness variations in hyperelasticity. Detailed mathematical derivations are presented for the computation of generalized incremental moduli, which are applied to both classical and recent isotropic hyperelastic models, including Neo-Hookean, Mooney-Rivlin, Fung-Demiray, and Anssari-Benam formulations. The analytical results reveal how strain-induced anisotropy evolves under different loading conditions, such as uniaxial, equibiaxial, and simple shear, highlighting model-dependent trends in stiffening and softening behavior. Overall, the study demonstrates that the proposed definition of generalized incremental moduli provides a comprehensive and versatile tool for the analysis of tangent stiffness in hyperelastic materials, with potential applications in material characterization and engineering design.