Mechanical properties of hierarchical lattices

• Four 2D and four 3D lattices with up to three hierarchic levels are analysed.
• The effects of multiple levels of hierarchy in lattices are quantified.
• Material charts for lattices with multiple hierarchic levels are presented.
• Multiple hierarchies improve buckling strength at the micro level.
• Multiple hierarchies promote stress concentrations that reduce the yield strength.

This paper focuses on the stiffness and strength of lattices with multiple hierarchical levels. We examine two-dimensional and three-dimensional lattices with up to three levels of structural hierarchy. At each level, the topology and the orientation of the lattice are prescribed, while the relative density is varied over a defined range. The properties of selected hierarchical lattices are obtained via a multiscale approach applied iteratively at each hierarchical level. The results help to quantify the effect that multiple orders of structural hierarchy produces on stretching and bending dominated lattices. Material charts for the macroscopic stiffness and strength illustrate how the property range of the lattices can expand as subsequent levels of hierarchy are added. The charts help to gain insight into the structural benefit that multiple hierarchies can impart to the macroscopic performance of a lattice.