A hyperelastic model for hollow fiber-reinforced composites at finite deformation

This study introduces a micromechanics-based constitutive model to describe the effective hyperelastic behaviors of hollow fiber-reinforced composites under finite deformation. The multiplicative decomposition approach is employed to decompose a general deformation into three fundamental deformations: isochoric uniaxial deformation along the fiber direction, equi-biaxial deformation on the transverse plane, and pure shear deformation. Based on this multiplicative decomposition, the free energy density function of the composites is thus additively decomposed into the three corresponding components. Subsequently, the effective free energy density functions of the composite for triaxial deformation (composed of the isochoric uniaxial deformation along the fiber direction and equi-biaxial deformation on the transverse plane), along-fiber shear, and transverse shear are derived using a cylindrical composite element model. The total free energy density function of the composite is then obtained by summing the contributions of these decomposed deformations. To validate the proposed model, finite element simulations based on representative volume elements are conducted. The effects of fiber volume fraction, fiber/matrix stiffness ratio, and wall thickness of hollow fiber on the effective mechanical behaviors of the composites are explored. The theoretical predictions show excellent agreement with numerical results for all considered cases, demonstrating that the proposed model reliably predicts the effective mechanical response of hollow fiber-reinforced composites under finite deformation. Finally, to further validate the prediction accuracy and computational efficiency of the developed model, it is applied to the structural analysis of a cantilever beam, with results compared to those obtained using the FE² method. This comparative analysis demonstrates again the accuracy and efficiency of the proposed approach in practical structural analysis.