An investigation of elastic properties of hierarchical honeycomb structures

Honeycombs are an example of cellular structures which are widely found in nature. Their lightweight and superior mechanical properties inspired engineers and scientists to use them in many areas such as architecture, material engineering, chemical engineering, and mechanical engineering. It has been recently found that mechanical properties of hexagonal structures can be improved by introducing new hierarchies to the structure [31]. Thus it is very important to understand how these mechanical properties are affected by the existence of the hierarchy and the changing of the hierarchy parameters. In this thesis, we studied analytically and numerically effective mechanical properties of two-dimensional regular honeycomb and hierarchical honeycomb structures. The main objective was to determine relevant hierarchy parameters which significantly improve effective mechanical properties of the structures. However, unlike previous studies which considered only hexagonal geometries, we investigated the effect of different geometries in the hierarchy which have been denoted as hybrid. In addition to the geometry of the hierarchy, we investigated the effect of heterogeneity by changing the wall thickness at different hierarchy levels. In our results, we found that by introducing a hierarchy, at least 2 times stiffer designs can be achieved compared to the ordinary hexagonal honeycombs having the same relative density. This study shows that effective elastic properties such as the Young's modulus and Poisson's ratio, of honeycomb structures can be controlled by changing hierarchy geometries and heterogeneity levels.