Hyperelastic Constitutive Modeling of Hexagonal Honeycombs Subjected to In-Plane Shear Loading

The in-plane flexible shear property of hexagonal honeycombs may be useful for the compliant structural applications. In this paper, hyperelastic strain energy functions are developed for a finite in-plane shear deformation of hexagonal honeycombs over a constituent material’s elastic range. Effective shear stress-strain curves of hexagonal structures and local cell wall deformation are investigated using the finite element based homogenization method. The hyperelastic models, which are only related to the effective properties of a honeycomb, may not be good enough to capture the nonlinear behavior at a high macroscopic shear strain level. The primary microscopic cell wall deformation mode under macroscopic in-plane shear loading was identified to be the bending of the vertical cell wall $h$⁠, which is perpendicular to the macroscopic loading direction. The re-entrant hexagonal structures having a negative Poisson’s ratio shows a high macroscopic shear flexible property associated with the high $h$ when the honeycombs are designed to have the same macroscopic shear modulus.