Variable Dual Auxeticity of the Hierarchical Mechanical Metamaterial Composed of Re‐Entrant Structural Motifs

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.

On the effect of the poisson’s ratio on samples subjected to shearing

“…At present, the most promising class of materials which could be used for such testing and verification are auxetic foams, but even here, large enough samples with Poisson's ratios approaching −1 where the pore size is small enough that the material can be seen as a solid rather than as a cellular structure are yet to become widely available. It is thus envisaged that tests to confirm these predictions will most likely be performed on samples which lack some of these ideal criteria, for example, foam samples which are slightly anisotropic and only reach Poisson's ratios of −0.5 rather than −0.90, or auxetic metamaterials [55][56][57] which may be rather porous. In this respect, an important strength of this work is that experimentalists now have a detailed list of specific features, such as the concave creases, that they should be on the lookout for when testing samples in shear.…”

Micro‐Scale Mechanical Metamaterial with a Controllable Transition in the Poisson's Ratio and Band Gap Formation

“…Last but not least, it is worth noting that it is possible to construct an active metamaterial composed of only one type of residual material that, to some extent, can undergo a change in its mechanical properties with a deformation pattern based solely on the variation of the mechanical stimulus, for example, the rate of mechanical compression. A prime example of this approach corresponds to hierarchical metamaterials, [ 59–65 ] where different hierarchical levels can deform independently of each other.…”

“…The most studied cases and well-known examples of metamaterials with extraordinary mechanical properties pertain to those with negative properties such as a negative Poisson's ratio (auxetic compression. A prime example of this approach corresponds to hierarchical metamaterials, [59][60][61][62][63][64][65] where different hierarchical levels can deform independently of each other.…”

A 3D re-entrant structural metamaterial with negative Poisson’s ratio reinforced by adding arrow structures

“…Other methods for enhancing the stiffness of auxetics such as composite materials [19] made of auxetic inclusions, the thickness gradient re-entrant honeycomb structure [20], and so on [14,21] are proposed. Besides, the negative Poisson's ratio and stiffness can be simultaneously changed by introducing hierarchical structure, such as re-entrant hierarchical honeycombs [22], the hierarchical mechanical metamaterial composed of re-entrant structural motifs [23] and a vertex-based hierarchical re-entrant honeycomb structure [24]. However, most of the above mentioned methods only are feasible for 2D RS, in which the negative Poisson's effect does not exhibit simultaneously in the out-ofplane direction.…”