Fracture toughness of hierarchical self-similar honeycombs

The influence of self-similar hierarchy on the brittle fracture behavior of a two-dimensional honeycomb is investigated. The honeycomb walls are modeled as Bernoulli-Euler beam elements rigidly connected at the nodal points, and zero, first and second order hierarchies are addressed. The stress state in the vicinity of a semi-infinite crack is determined, and the fracture toughness is calculated in terms of tensile strength of parent material. The growth of hierarchical order leads to increase in the number of nodal degrees of freedom to be taken into account, and the computational cost of the calculations is reduced by employing a novel analysis method based on the discrete Fourier transform. An increase in hierarchical order enhances the fracture toughness after optimization of geometrical parameters at fixed relative density. This effect becomes more pronounced for honeycombs of lower relative density. (C) 2018 Elsevier Ltd. All rights reserved.