Gradient re-entrant honeycomb with quasi-ZPR and improved out-of-plane flexibility through tunable horizontal ligaments

Flexible skins for morphing aircraft wings rely on honeycomb cores to adapt to aerodynamic shapes. However, the out-of-plane flexibility of the conventional re-entrant honeycomb (CRH) cannot be improved without compromising flatwise stiffness. To overcome this limitation, a novel gradient re-entrant honeycomb (GRH) design that incorporates horizontal ligaments is introduced. A multiscale constitutive framework is established using the variational asymptotic method to model complex GRH structures. This framework results in a three-dimensional equivalent Cauchy model (3D-ECM) for multicellular GRH and a two-dimensional equivalent plate model (2D-EKM) for GRH panels. The efficacy and accuracy of these equivalent models are confirmed through uniaxial compression and tensile tests on 3D printed multicellular GRH specimens, complemented by numerical simulations evaluating the out-of-plane and in-plane behaviors of GRH panels. Compared to the CRH, the GRH demonstrates a 23.0% reduction in out-of-plane elastic modulus and a 66.7% increase in in-plane elastic modulus. The optimal GRH parameters — re-entrant angle of 80°, horizontal ligament-to-inclined wall length ratio of 1.2, wall thickness ratio of 0.15, and horizontal ligament-to-cell height ratio of 0.4 — ensure high in-plane stiffness, out-of-plane flexibility, quasi-ZPR, and low effective density, making the structure ideal for lightweight, high-performance applications.