Multi-objective parametric optimisation of architected hexagonal honeycomb with stepped struts

Recent advances in small-scale fabrication enable the creation of architected metamaterials with tailored mechanical properties by manipulating their structures at the micro and nanoscale. In this study, the shape of 2D hexagonal honeycombs is modified by redistributing solid material to create stepped struts with two thicknesses. Analytical expressions are derived to show the effect of the geometric parameters on the unit cell stiffness, buckling and plastic strengths. An analytical multi-objective optimisation is performed to find the design parameters that simultaneously maximise stiffness and strength in the range of relative densities of cellular solids. Theoretical results show that a stepped strut can simultaneously enhance the stiffness of the uniform honeycomb by 36.3% and the plastic strength by 36.5%. For low relative densities, redistributing material does not significantly enhance the buckling strength of the uniform hexagonal architecture, but a stiffness gain of 29.1% is observed. Failure maps are provided to assess the influence of relative density and design parameters on the lattice failure mode. The analytical results are validated by finite element modelling and experiments, showing excellent agreement. Therefore, the study demonstrates a parametric shape optimisation approach, which can be extended to enhance the performance of other 2D and 3D mechanical metamaterials. • Analytical derivation of the stiffness, plastic and buckling strength scaling laws for hexagonal honeycombs with stepped struts, validated numerically and experimentally. • Multi-objective parametric optimisation of stepped-strut hexagonal lattices shows the relative density- and failure mode-dependent domain of Pareto optimal configurations that maximise the lattice stiffness and strength. • The solid material redistribution through a stepped profile leads to a simultaneous increase of stiffness and plastic strength by 36% with respect to regular honeycombs. • Failure maps showing the interplay between geometric parameters, relative density and failure modes are provided. • The studied solid material redistribution changes the lattice failure mode and can induce a strain-dependent auxetic response.