The influence of tapered cell walls on the stiffness and strength of hexagonal honeycombs under uniaxial and biaxial loading

This study highlights the potential of leveraging solid material redistribution through tapered cell walls to enhance the stiffness and strength of regular hexagonal honeycombs. The investigation includes analytical derivation of the stiffness, buckling stress, plastic strength and yield domain of honeycomb with tapered struts subjected to uniaxial, shear and biaxial in-plane loading, benchmarking them against the properties of uniform hexagonal honeycombs, to highlight the effects of linearly varying thickness in the cell walls. Furthermore, for uniaxial loading, the influence of geometric design parameters and relative density is assessed to define the dominant failure mode between elastic buckling and plastic failure and to select the optimal tapered profile among the Pareto optimal solutions that simultaneously enhance stiffness and strength. For biaxial loading, the geometry-dependent equivalent stiffness is computed including axial effects and compared with that of the uniform tapered uniaxial counterparts, while the yield domain is obtained considering different failure mechanism. Finite element analyses and experiments on polymeric and stainless steel lattices with different relative densities are carried out to validate the analytical findings. The results show how tapered struts increase the stiffness and strength of uniform honeycombs under all in-plane loading conditions assessed, except when the loading approaches equibiaxial conditions. At low relative densities undergoing elastic instabilities, the uniaxial stiffness of the uniform honeycomb can be enhanced by 40.1% without compromising the buckling strength, while above the critical relative density, the uniaxial stiffness and strength can be simultaneously increased by 61.2% and 97.7%. Similarly, it is shown that tapered honeycombs optimised for uniaxial loading can also offer an increase in shear and biaxial properties, with an increase in stiffness and expansion of the yield domain for most of stress biaxiality ratios. These gains are primarily due to increased nodal resistance and a more efficient material arrangement that follows the stress distribution, which delays the onset of failure and enhances overall structural integrity. The analytical results and the gains achievable by tapered honeycombs represent valuable insights for engineering applications requiring lightweight, high-specific stiffness and strength materials.