Variable Dual Auxeticity of the Hierarchical Mechanical Metamaterial composed of Re-entrant Structural Motifs

TL;DR

This paper introduces a hierarchical mechanical metamaterial with re-entrant motifs that exhibits variable dual auxeticity, tunable deformation mechanisms, and controllable wave propagation properties, useful for vibration damping and biomedical applications.

Contribution

It presents a novel hierarchical design enabling dual auxetic behavior and tunable wave transmission, advancing the control of mechanical and acoustic properties in metamaterials.

Findings

The structure exhibits variable auxetic behavior depending on hinge thickness.

Different hierarchical levels show distinct auxetic deformation mechanisms.

Small design changes significantly affect wave band gaps.

Abstract

In this work, a novel hierarchical mechanical metamaterial is proposed that is composed of re-entrant truss-lattice elements. It is shown that this system can deform very differently and can exhibit a versatile extent of the auxetic behaviour depending on a small change in the thickness of its hinges. In addition, depending on which hierarchical level is deforming, the whole structure can exhibit a different type of auxetic behaviour that corresponds to a unique deformation mechanism. This results in a dual auxetic structure where the interplay between the two auxetic mechanisms determines the evolution of the system. It is also shown that depending on the specific deformation pattern, it is possible to observe a very different behaviour of the structure in terms of frequencies of waves that can be transmitted through the system. In fact, it is demonstrated that even a very small change in the parametric design of the system may result in a significantly different band gap formation that can be useful in the design of tunable vibration dampers or sensors. The possibility of controlling the extent of the auxeticity also makes the proposed metamaterial to be very appealing from the point of view of protective and biomedical devices.