Mechanical properties of hierarchical honeycomb structures

Abstract

Cellular solids such as foams are widely used in engineering applications mainly due to their superior mechanical behavior and lightweight high strength characteristic. On the other hand, hierarchical cellular structures are known to have enhanced mechanical properties when compared to regular cellular structures. Therefore, it is important to understand the mechanical properties and the variation of these properties with the presence of hierarchy. This investigation builds upon prior works and considers the mechanical properties of two dimensional hierarchical honeycomb structures using analytical and numerical methods. However, in contrast to previous research, the hierarchy in this work is constructed by replacing every three edge vertex of a regular hexagonal honeycomb with a smaller hexagon. This gives a hierarchy of first order. Repeating this process builds a fractal appearing second order hierarchical structure. Our results showed that hierarchical honeycombs of first and second order can be up to 2 and 3.5 times stiffer than regular hexagonal honeycombs with the same relative density.