Spiderweb Honeycombs

Abstract

Small and large deformation in-plane elastic response of a new class of hierarchical fractal-like honeycombs inspired by the topology of the “spiderweb” were investigated through analytical modeling, detailed numerical simulations, and mechanical testing. Small deformation elasticity results show that the isotropic in-plane elastic moduli (Young’s modulus and Poisson’s ratio) of the structures are controlled by dimension ratios in the hierarchical pattern of spiderweb, and the response can vary from bending to stretching dominated. In large deformations, spiderweb hierarchy postpones the onset of instability compared to stretching dominated triangular honeycomb (which is indeed a special case of the proposed spiderweb honeycomb), and exhibits hardening behavior due to geometrical nonlinearity. Furthermore, simple geometrical arguments were obtained for large deformation Poisson’s ratio of first order spiderweb honeycombs, which show good agreement with numerical and experimental results. Spiderweb honeycombs exhibit auxetic behavior depending on the non-dimensional geometrical ratio of spiderweb.