3D compression–torsion cubic mechanical metamaterial with double inclined rods

Abstract

A novel 3D compression–torsion cubic mechanical metamaterial (CTCMM) with double inclined rods is proposed converting axial compression into a torsion. The CTCMM under uniaxial compression is studied by theoretical analysis, experiments and numerical simulations. The relationships between relative densities and geometric parameters are analyzed to meet the needs of lightweight. Based on the derivation of the over-deformation mechanism, the torsion angle is derived by the Timoshenko beam theory. The arrangements of gradient models are designed and fabricated by 3D printing, as the specimens for static compression experiments. Results show that the torsion angles of the numerical and experimental results agree well with the theoretical solution. Moreover, the proposed CTCMM possesses a similar compression–torsion effect compared to previously reported 3D CTCMM. Meanwhile, the improved 3D CTCMM with the better compression–torsion effect is proposed, compared with the original structure, the different phenomenon wherein the torsion angle first increases and then declines. Finally, cell number, variable cross-section and perforated plates all affect the compression–torsion effects of 3D CTCMM. The above research provides a new idea for improving the performance of CTCMM, no longer limited to the deformation mode of a single inclined rod.

Introduction

In recent decades, scholars have enriched the mechanical metamaterials library with large amounts of novel and excellent structures. Mechanical metamaterials are divided into: re-entrant honeycomb structure [1], [2], [3], [4], rotating rigid structure [5], [6], chiral structure [7], [8], [9], perforated plate structure [10], node fiber structure [11] and other structures [12] on the basis of different deformation mechanisms. Owing to the significantly deformation and simple construction, this structure can potentially be useful in sensors, actuators [1] and energy absorption [4] applications. Thus, the re-entrant structures have appeared abundant novel structures. Huang et al. [1] added the plates to re-entrant structures and provide separate contributions to the in-plane and out-of-plane mechanical property. Xiao et al. [4] presented a detailed study of the NPR effect on shrinkage deformation and crushing stress of metallic auxetic reentrant honeycomb under low, medium and high-velocity compressions. Wang et al. [13]. established the analytical model of 3D re-entrant auxetic cellular structure, and consider the overlapping of the struts as well as axial extension or compression. Fu et al. [14] enhanced in-plane stiffness and buckling strength by adding cross rods. Besides, double-arrow honeycomb structures [15] and star-shaped structures [16], [17] also was discussed continually. It is worth noting that structure is related to special re-entrant angle, but the shape of the re-entrant angle is not a sufficient condition for the negative Poisson’s ratio (NPR) structure [16].

Furthermore, the combination of NPR with other indicators, such as negative stiffness [18], negative compressibility, negative stability, and negative thermal expansion [19], [20], [21], is also exceedingly popular. Traditional 3D-NPR structures [13], [22] often adopt isotropic structures, instead of adopting different deformation mechanisms to achieve fancy structures. The compression–torsion​ structure with rotational characteristics is consists of a consistent unit cell on different surfaces when proposed firstly [23]. The compression–torsion structures developed later mainly adopt the twist chirality of a single direction, generating the whole structure produces a twist effect [24], [25], [26] during axial compression. Zhong et al. [24] proposed a 3D compression–torsion mechanical metamaterial, which has larger torsion angle in a direction. Li et al. [25] developed with the inspiration of the shear–compression coupling effect of the 2D materials, and explore the compression–torsion metamaterials. Chen et al. [26] adopted a systematic topology optimization approach into designing materials of tubes, and obtained the tube with multihole. Although the compression–torsion mechanical metamaterials have been studying in recent years, better oblique bar models are still rarely reported.

In this paper, a novel CTCMM with double inclined rods is presented. The expressions of relative density and torsion angle are deduced by establishing a theoretical model. The correctness of theoretical prediction is verified by experiments and finite element simulations. The variable section compression–torsion structure are discussed to enrich the types of metamaterials. These conclusions provide different extension ideas for sensors and actuators.