Parametric optimization of corner radius in hexagonal honeycombs under in-plane compression

What is the optimum corner radius for a regular hexagonal honeycomb in the context of in-plane, quasistatic compression loading? Drawing inspiration from social insect hexagonal cell nests, where a non-zero corner radius appears to be a design feature, a 400-point design of experiments study is conducted using 2D plane strain Finite Element Analysis (FEA) to study the influence of cell size, beam thickness and corner radius on effective modulus and maximum corner stress in the honeycomb cells. An experimental study is conducted to examine these relationships beyond the bounds of the small deformation, linear elastic FEA analysis. The study finds that corner radii always increase the effective modulus of the honeycomb, even after accounting for the additional mass associated with the corner fillet. A key finding of this work is that while corner radii also reduces the maximum corner stress, there exists a clear optimum, beyond which stresses rise again as the corner radius increases in magnitude. This optimum corner radius is shown to be a function of the beam thickness (t) to beam length (l) ratio (t/l), with the optimum value increasing with increasing t/l. The experimental study shows that the presence of a corner radius shifts the failure mechanism from nodal fracture to plastic hinging for honeycombs with thick beams, and may have benefits for energy absorption applications. This work makes the case for the treatment of the corner radius as an independent design feature for optimization in the wider context of cellular materials, as well as has implications for the study of the geometry of insect nests.