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

Abstract

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.