Hybrid hierarchical square honeycomb with widely tailorable effective in-plane elastic modulus

Abstract

In this study, a hybrid hierarchical square honeycomb (HHSH) is proposed, and its effective in-plane elastic modulus is investigated theoretically and numerically. The HHSH is proposed by replacing each vertex of an edge-based hierarchical square honeycomb (EHSH) with a smaller diamond, where the EHSH is constructed by replacing each solid cell wall of a regular square honeycomb (RSH) with smaller squares. The proposed HHSH integrates the geometric features of both edge-based and vertex-based hierarchical honeycombs. A theoretical model for the effective in-plane elastic modulus of HHSH is developed, and it is validated with experimental and numerical results. By using theoretical and numerical methods, the effect of structural parameters and relative density on the effective elastic modulus is analyzed. Results show that the HHSH has a robust ability to tailor the effective elastic modulus. The unique ability is mainly attributed to the multiple structural parameters introduced by both the edge-based and vertex-based hierarchy. This study provides a novel strategy for the design of hierarchical honeycombs with widely tailorable mechanical properties.