Mechanical Properties of Hierarchical Honeycomb Structures

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.;Another mechanical property considered in this study is the energy absorbance of hierarchical honeycombs. The in-plane dynamic crushing of hierarchical cellular structures is yet to be investigated. Most of the previous work performed on the mechanical behavior of cellular materials, considers an intact structural organization for the cellular material. Thus, to further explore the energy absorbance of hierarchical honeycombs, we have studied the response of three dimensional regular hexagonal first order hierarchical honeycombs under in-plane dynamic crushing. Finite element method was employed to measure the response of hierarchical cellular structures under impact loading. As it is well established, honeycomb cellular structures behave differently under dynamic loading, mainly in their deformation modes and stress levels. In addition, for plastic behavior, the bilinear material properties with two different hardening rates (5% and 10%) were also considered. Our results demonstrate that there is not much difference in the energy absorption of the hierarchical structures when compared to regular honeycombs for elastic perfectly plastic material. However, by applying strain hardening to the material that makes up the cell walls of the hierarchical honeycomb, the energy absorbance of the structures significantly increases.