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Various honeycomb structures to be subjected to in-plane axial compression as shown in the next image

(a) From left to right: Regular honeycomb, hexagonal hierarchical honeycomb, Kagome hierarchical honeycomb, and triangular hierarchical honeycomb
(b) Representative volume element of each type of honeycomb
(c) The corresponding cell wall of each type of honeycomb

r is thr ratio of the length of the side of one of the sub-honeycombs to that of the main honeycomb

This and the next 4 images are from:

Hanfeng Yin (1), Xiaofei Huang (1), Fabrizio Scarpa (2), Guilin Wen (1), Yanyu Chen (3) and Chao Zhang (4)
(1) Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, Hunan, China
(2) Bristol Composites Institute (ACCIS), University of Bristol, Bristol BS8 1TR, UK
(3) Transportation and Hydrogen Systems Center, National Renewable Energy Laboratory, Golden, CO, USA
(4) School of Aeronautics, Northwestern Polytechnical University, Xi’an, Shanxi, China

“In-plane crashworthiness of bio-inspired hierarchical honeycombs”, Composite Structures, Vol. 192 pp 516-527, May 2018

ABSTRACT: Biological tissues like bone, wood, and sponge possess hierarchical cellular topologies, which are lightweight and feature an excellent energy absorption capability. Here we present a system of bio-inspired hierarchical honeycomb structures based on hexagonal, Kagome, and triangular tessellations. The hierarchical designs and a reference regular honeycomb configuration are subjected to simulated in-plane impact using the nonlinear finite element code LS-DYNA. The numerical simulation results show that the triangular hierarchical honeycomb provides the best performance compared to the other two hierarchical honeycombs, and features more than twice the energy absorbed by the regular honeycomb under similar loading conditions. We also propose a parametric study correlating the microstructure parameters (hierarchical length ratio r and the number of sub cells N) to the energy absorption capacity of these hierarchical honeycombs. The triangular hierarchical honeycomb with N = 2 and r = 1/8 shows the highest energy absorption capacity among all the investigated cases, and this configuration could be employed as a benchmark for the design of future safety protective systems.

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