Tetrachiral Honeycombs Research Articles

A Novel Cross Tetrachiral Honeycomb Metamaterial with Designable Static and Dynamic Performances.

A novel cross tetrachiral honeycomb metamaterial is proposed, which not only possesses the negative Poisson's ratio property, but also has a wide-frequency bandgap. The effective elastic parameters of the cross tetrachiral honeycomb are first theoretically analyzed; then, its designable performances for negative Poisson's ratio and elastic modulus are studied by varying geometric parameters. The dynamic properties of the cross tetrachiral honeycomb metamaterial are investigated by analyzing the band structure. It is shown that without the addition of external mass to the structure, a designable wide bandgap can be generated to isolate the in-plane waves effectively by selecting the ligament angles and the radius of central cylinder. In addition, an effective approach is proposed for tuning the bandwidth without changing the geometric parameters of the structure. Compared to classical negative Poisson's ratio metamaterials, the proposed cross tetrachiral honeycomb metamaterial is designable and tunable for achieving a specific static or dynamic performance, and has potential applications in engineering practice.

Clockwise vs anti-clockwise chiral metamaterials: Influence of base tessellation symmetry and rotational direction of chiralisation on mechanical properties

Chiral honeycombs are a class of auxetic metamaterials which are characterised by a lack of plane symmetry. Besides the traditional chiral honeycombs based on regular monohedral tessellations such as the hexachiral and tetrachiral honeycombs, a vast range of auxetic chiral metamaterials may be produced through the ‘chiralisation’ of Euclidean tessellations made from polyhedral tilings and/or irregular monohedral polygons. In this work, we show for the first time, how the direction of the geometric chiral transformation, i.e. clockwise vs anti-clockwise chiralisation, has an influence on the mechanical properties and deformation modes of the resultant chiral metamaterial systems. This influence, which is a result of the intrinsic absence of axial symmetry in the original base tessellation, can lead to the production of two unique and distinct chiral metamaterial configurations with completely different mechanical properties originating from a single base tessellation. In this work we demonstrate and quantify, through a wide range of numerical simulations and experimental tests on additively-manufactured prototypes, the effect of the direction of chiralisation on two tessellations: a Florent pentagonal system with hexagonal rotational symmetry and a hexagonal monohedral tessellation with trigonal rotational symmetry. The results obtained show that the clockwise and anti-clockwise chiral structures exhibit significantly different mechanical properties and deformation modes, highlighting the increased versatility of this relatively novel class of chiral metamaterials.

Energy absorption characteristics and negative Poisson's ratio effect of axisymmetric tetrachiral honeycombs under in-plane impact

Negative Poisson’s ratio honeycombs have been widely studied in recent years due to their unique mechanical properties. A tetrachiral honeycomb (TCH) exhibits a bulging effect when subjected to in-plane impact, reducing its Poisson’s ratio effect. To improve the performance of TCH, this study proposes two types of axisymmetric tetrachiral honeycombs (ATCH-1 and ATCH-2). First, the in-plane impact performances of TCH, ATCH-1, and ATCH-2 are compared via experiments, and the accuracy of the finite element model is validated. Then, the effects of the different parameters on the deformation modes, energy absorption characteristics, and negative Poisson’s ratio effects of the three types of honeycombs are analyzed via finite element models. ATCH-1 and ATCH-2 have higher specific energy absorption (SEA) and a more significant negative Poisson’s ratio effect than TCH at an impact velocity of 10 m/s. However, the axisymmetric honeycombs do not have advantages at impact velocities of 50 m/s and 100 m/s. The cylindrical radius r significantly affects the deformation mode of the three types of honeycombs. The axisymmetric design provides a new concept for the novel negative Poisson's ratio honeycomb design.

Tetrachiral honeycomb regulated polymer-derived SiFeOC ceramics with tunable piezoresistive effect

Sensitivity-adjustable piezoresistive SiFeOC ceramic with tetrachiral honeycomb structures has been presented for pressure detection under harsh environments. The 3D structuralized piezoresistive structures exhibited marked structure-dependent sensing performance, providing another dimension for detection limit and sensitivity tunning. Digital light processing technique printed the Fe-doped SiOC tetrachiral honeycombs, in which Fe acted as a dopant for conductivity modification. Due to the activation of the percolation network consisting of free carbon in an amorphous matrix, the conductivity of the SiFeOC sensing structure reached 3.08 S/m. Meanwhile, the sensitivity of the structures can be optimized by adjusting rotation angles due to the negative Poisson's ratio (NPR) characteristics that provided tunable modulus, leading to a rise in the gauge factor from 169 to 796. The rotation angle adjustment also optimized the mechanical performance of the sensing structure, yielding a compression strength of 24.11 MPa. The robustness in load-bearing capacity also ensured long-term cyclic detection stability, realizing an intelligent piezoresistive structure with high strength and environmental tolerance.

In-plane dynamic crushing of a novel hybrid auxetic honeycomb with enhanced energy absorption

Recently, auxetic honeycombs have attracted widespread attention with characteristics of lightweight, excellent energy absorption capacity and high shear stiffness. The present paper proposes the hybrid star-shaped tetra-chiral honeycomb (STCH) by embedding the tetra-chiral honeycomb (TCH) into the star-shaped honeycomb (SSH). The deformation mode and compression behavior of the STCH were studied numerically and compared with that of the SSH and TCH. Particularly, under the impact velocity of 2 m/s, the specific energy absorption (SEA) of the STCH increases by 80 and 179% than that of the SSH and TCH, respectively. Through investigating the effect of impact velocity and relative density on the crushing behavior of the STCH, the deformation modes map was summarized, and the empirical formula of the plateau stress was presented. Subsequently, the detailed parameter analysis of the STCH revealed that in a certain range, the SEA and stability of the STCH increase with the increase of N x , θ , and R , and with the decrease of L 2 and L 1 . Finally, the improved STCH (ISTCH) with stable deformation and better crashworthiness was further proposed, and the crashworthiness of it was comprehensively compared with other structures. The result shows the excellent crashworthiness of the ISTCH. Particularly, the SEA of ISTCH can be nearly 8 times higher than that of the TCH.

The stressed state of three-layer composites with tetrachiral honeycombs under bending conditions: Mathematical modeling and additive manufacturing laboratory experiments

The stressed state of three-layer composites with tetrachiral honeycombs under bending conditions: Mathematical modeling and additive manufacturing laboratory experiments

A novel monoclinic auxetic metamaterial with tunable mechanical properties

Missing rib auxetics with a reinforced central core may have tunable negative Poisson's ratios (NPRs) and other mechanical parameters. In analogy with the other enhanced missing rib configurations (e.g., enhanced hexa-, anti-tri- and anti-tetra-missing rib honeycombs), a novel enhanced tetra-missing rib honeycomb metamaterial is proposed in this work. Similar as the classical tetra-chiral honeycomb, the proposed enhanced tetra-missing rib honeycomb metamaterial also exhibits monoclinic property, i.e., undergoing coupled shearing and stretching/shrinking under monotonic tension/compression. To facilitate the understanding of the underlying microstructural mechanisms, a theoretical model under the infinitesimal deformation assumption is developed by a simple energy-based approach. The obtained analytical solutions are validated by systematic finite element (FE) analyses conducted for a unit-cell with periodic boundary conditions, and elucidate different roles of the microstructural geometry on the effective mechanical properties of the proposed metamaterial. It is shown that the proposed metamaterial exhibits tailorable Poisson's ratios (from -1 to 0) as well as elastic (over five orders of magnitude) and shear moduli (over four orders of magnitude) in wide ranges. Compared with the previously developed enhanced anti-tetra-missing rib honeycomb, which has the same building block as the proposed design in this paper, the stiffness of the present design is improved remarkably with the same geometrical parameters owing to its monoclinic property. The improvement can even reach two orders of magnitude in some cases. Uniaxial tensile experimental tests and finite-size FE simulations for the proposed metamaterial structures consisting of an array of unit-cells are also performed to validate the theoretical and FE results obtained from the unit-cell analyses.

Numerical analysis of the stressed state of composite plates with a core layer made of tetrachiral honeycombs under static bending

The present work considers three-layer composite plates with solid face layers and a honeycomb core layer of the tetrachiral type. Under static bending conditions, the effects of discretization (the number of unit cells), relative density and thickness of tetrachiral honeycombs on the stressed state of composite plates are studied. Two sets of numerical experiments have been conducted: within the first one, the thicknesses of layers of composite plates have been remained constant with the variation in the volume of solid body of honeycombs, and in the second case, the volume of solid body of honeycombs is constant under the variation in the thickness of the honeycomb structures. Numerical modeling has been carried out within the framework of the theory of elasticity using the Comsol Multiphysics finite element analysis software, as well as with help of the finite element algorithms for solving the plane problem of the theory of elasticity. Based on the results of the analysis, diagrams of the honeycomb core relative density and thickness dependence of the maximal stresses in the layers of composite plates are presented, respectively, for the first and second formulation of numerical experiments. It has been shown that the discretization of tetrachiral honeycombs provides a significant effect on the strength of the honeycombs. Variation in the honeycombs thickness via changing the relative density under the constant volume of honeycombs solid body also has a significant effect on the strength of the composites.

STATIC BENDING STRENGTH OF SANDWICH COMPOSITE PLATES WITH TETRACHIRAL HONEYCOMBS

The article presents a numerical strength analysis of sandwich plates with solid face layers and tetrachiral honeycomb core layer under static bending conditions. An aluminum alloy was chosen as the material of plates. For honeycomb core layers, the discretization (number of unit cells) and the relative density were varied with a constant thickness. Calculations were performed for the case of bending with rigidly clamped ends and three-point bending within the framework of the theory of elasticity by the finite element method. The strength analysis enables one to determine the load values, at which the maximal stresses according to the von Mises criterion were equal to the conventional yield stress of the material. The aim of this work is to study the effect of discretization and relative density of honeycomb core layers of tetrachiral type on the str ength of sandwich plates.

A Novel Strategy for Constructing 3D Dislocated Chiral Metamaterial with Negative Poisson's Ratio

Metamaterials with negative Poisson's ratio (NPR) have a broad range of application background, such as aerospace engineering, automotive engineering, medical instrument engineering, and wearable engineering. Herein, a novel strategy for constructing 3D dislocated chiral metamaterial is proposed that can achieve NPR effect in three directions. According to this strategy, a new dislocated chiral metamaterial composed of dislocated tetrachiral honeycombs and inclined rods is designed and selected as an example to investigate the effectiveness of the strategy. Experiments and numerical simulations are carried out to study the mechanical properties of the new metamaterial, confirming that this metamaterial exhibits NPR effect. The influence of geometric parameters on the elastic constants of the metamaterial is discussed based on experimental and numerical results. Meanwhile, the local loading performances of this dislocated chiral metamaterial and the previous aligned chiral metamaterial are studied and compared. Results show that this dislocated metamaterial possesses a stronger damage resistance capacity than the aligned one. By adjusting the rotational direction of ligaments in honeycombs and the arrangement of inclined rods, more special 3D dislocated chiral metamaterials with advanced properties are available, such as metamaterial with both positive and NPRs, metamaterial with compression–torsion effect.

Dynamic performance of auxetic structures: experiments and simulation

In this study, the in-plane mechanical properties of auxetic structures subjected to dynamic compression have been investigated experimentally and numerically. The studied auxetic structures, which have negative Poisson’s ratios, include a recently developed auxetic structure named re-entrant chiral auxetic (RCA) structure, re-entrant honeycomb, tetrachiral honeycomb and anti-tetrachiral honeycomb. All structures studied were fabricated from polyamide12 (PA12) powder using multi jet fusion. Compressive tests were conducted at a constant crushing velocity of 5 m s−1 on an Instron VHS 8800 high speed testing machine. The experimental results showed that the RCA structure crushed in the Y direction offered better energy absorption capacity than the other three types of honeycomb. It was also found that loading direction had a significant influence on deformation modes and auxetic features of the RCA structure, while it had a moderate influence on the energy absorption capacity. Numerical models were developed using ABAQUS/explicit and verified by experimental results. Parametric study was conducted to investigate the effects of crushing velocity and geometrical parameters on the dynamic performance of the RCA structure.

Auxeticity of monoclinic tetrachiral honeycombs

Chiral honeycombs of different types have been found to display auxetic behavior (a negative Poisson’s ratio). This paper investigates the constitutive relations and the auxetic properties of tetrachiral honeycombs. It is found that coupling between shearing and stretching exists in tetrachiral honeycombs and this causes some ambiguity when calculating the Poisson’s ratio. An “effective Poisson’s ratio” is proposed, as opposed to the traditional definition of Poisson’s ratio. This proposed parameter correctly describes the auxeticity of tetrachiral and other honeycombs. An analytical expression for this “effective Poisson’s ratio” is derived, which describes the relationship between the geometric dimensions and auxeticity of the tetrachiral honeycombs.

Compressive properties of 3D printed auxetic structures: experimental and numerical studies

ABSTRACT Metamaterials that exhibit negative Poisson’s ratio (NPR) are known as auxetics. They laterally expand or contract when they are axially tensioned or compressed. A re–entrant chiral auxetic structure (RCA) is a recently developed structure, which combines the topological features of re–entrant and chiral honeycombs. Comparative study between the RCA structure and popular benchmarks subjected to uniaxial compression has been conducted experimentally and numerically. Specimens have been fabricated from polyamide12 (PA12) using Multi Jet Fusion (MJF). Numerical models have been developed using ABAQUS/Explicit and verified by the experiments. The experimental measurements manifest the high accuracy of the MJF process to produce robust components with precise details. It has been found that the RCA structure outperforms the other types of honeycombs in terms of strength and specific energy absorption when loaded in the Y direction, while only the tetrachiral honeycomb surpasses the RCA structure in terms of specific energy absorption when loaded in the X direction. The auxeticity (NPR) of the RCA structure compressed in the Y direction was larger than that of the other honeycombs. Numerical models have been employed to study the effects of friction and the number of cells on the mechanical response of the RCA structure.

A novel layered topology of auxetic materials based on the tetrachiral honeycomb microstructure

Microstructured honeycomb materials may exhibit exotic, extreme and tailorable mechanical properties, suited for innovative technological applications in a variety of modern engineering fields. The paper is focused on analysing the directional auxeticity of tetrachiral materials, through analytical, numerical and experimental methods. Theoretical predictions about the global elastic properties have been successfully validated by performing tensile laboratory tests on tetrachiral samples, realized with high precision 3D printing technologies. Inspired by the kinematic behaviour of the tetrachiral material, a newly-design bi-layered topology, referred to as bi-tetrachiral material, has been theoretically conceived and mechanically modelled. The novel topology virtuously exploits the mutual collaboration between two tetrachiral layers with opposite chiralities. The bi-tetrachiral material has been verified to outperform the tetrachiral material in terms of global Young modulus and, as major achievement, to exhibit a remarkable auxetic behaviour. Specifically, experimental results, confirmed by parametric analytical and computational analyses, have highlighted the effective possibility to attain strongly negative Poisson ratios, identified as a peculiar global elastic property of the novel bi-layered topology.

In-plane crushing response of tetra-chiral honeycombs

Tetra-chiral (TC) honeycombs are a type of auxetic materials showing negative Poisson's ratio (NPR), which are promising for impact energy absorption. This study aims to analyze the in-plane crushing response of the TC honeycombs under both quasi-static and dynamic loading conditions through numerical simulations and theoretical analyses. The numerical modeling techniques in LS-DYNA were validated using the quasi-static crush test data of TC honeycomb specimens obtained with a 3D-printer. Numerical simulations revealed the “Z” mode deformation and the “bulge effect” under quasi-static crushing, and the row-by-row “I” mode deformation under dynamic crushing of the TC honeycombs. By referring to the simulation results, theoretical models were derived based on the representative unit for predicting the TC honeycomb's crushing strength, i.e. plateau stress, under both quasi-static and dynamic loads. Good agreement was found between the theoretical and the numerical predictions with a maximum relative error of 7%. Parametric analyses showed that the unit cell configuration has a great effect on the crushing strength of TC honeycomb under in-plane crushing. The dynamic sensitivity index was defined to quantitatively evaluate the sensitivity of the TC honeycomb's crushing strength to the loading speed, and was found to depend on the unit cell geometry. The TC honeycomb was found to present a varied effective Poisson's ratio (EPR) with strain under both quasi-static and dynamic in-plane crushing; smaller radius ratio and lower crushing speed were found to yield more obvious NPR effect. Moreover, relative dimension of the TC honeycomb represented by the orthogonal array ratio do not affect its plateau stress under either quasi-static or dynamic crushing, while large orthogonal array ratio results in more obvious “bulge” and NPR effects under quasi-static crushing.

Special characteristics of tetrachiral honeycombs under large deformation

The nonlinear mechanical responses of tetrachiral honeycombs under large deformation are theoretically analyzed by employing elliptic integrals, and the results are verified by numerical simulations. The nonlinear relationships between normal stress, shear stress, Poisson's ratio and the strain are derived for the tetrachiral honeycombs. It is found that the Poison's ratio of the tetrachiral honeycombs under large deformation is totally different from that under small deformation. The Poisson's ratio can achieve to a large magnitude of 0.8 in the former case, while remains 0 in the latter case. Moreover, the tetrachiral honeycombs exhibit positive Poison's ratio under large tensile-deformation, whilst showing negative Poisson's ratio under large compression-deformation. The magnitude of Poisson's ratio depends on both the honeycomb's deformation and the ligament relative length, while it is insensitive to the ligament thickness. Besides, the coupling effect between tensile (or compression) and shear is observed for the tetrachiral honeycombs. In other words, shear deformation appears within the honeycomb under uniaxial loading. The coupling effect depends on both the honeycomb's deformation and the geometric parameters of the cell structure. And the quantitative relationships among them are derived. This special coupling effect of tetrachiral honeycombs provides a new idea for designing more metamaterials.

A novel category of 3D chiral material with negative Poisson's ratio

A new design thought for 3D auxetic material is proposed based on the rotaion mechanism of chiral honeycombs. Two kinds of cell shape of the 3D auxetic material are studied as example, which are developed from the tetrachiral honeycombs with circular loops and square loops, respectively, with inclined rods connecting the neighbor layers. By replacing the tetrachiral honeycomb layers by other chiral honeycombs, such as trichiral, hexachiral honeycombs, other kinds of 3D chiral material with negative Poisson's ratio can be obtained. Moreover, since the cells' deformation of the 3D material is dominated by that of ligaments and rods under small deformation, the elastic properties of the 3D auxetic material are almost independent of the loops' shape. Thus, the loop can be designed to any shape instead of the traditional circular loop in order to obtain priory mechanical properties under large deformation. Based on beam theory and micromechanical method, the analytical formulas of both the elastic mudulus and Poisson's ratio are deduced for this category of 3D chiral material, which are verified by numerical simulations but also the experiment of 3D printed model. The verification results indicate that the formulas have higher precision and wider application scope. The influence of layer space on the equivalent parameters and the conditions for isotropic realization are discussed base on the analytical formulas. By changing the oblique direction of the inclined rods, another new 3D material can be obtained with positive Poisson's ratio in two directions and negative Poisson's ratio in the other one direction, for which the analytical formulas are still applicable.

Homogenization of periodic hexa- and tetrachiral cellular solids

The homogenization of periodic hexachiral and tetrachiral honeycombs is dealt with two different techniques. The first is based on a micropolar homogenization. The second approach, developed to analyse two-dimensional periodic cells consisting of deformable portions such as the ring, the ligaments and possibly a filling material, is based on a second gradient homogenization developed by the authors. The obtained elastic moduli depend on the parameter of chirality, namely the angle of inclination of the ligaments with respect to the grid of lines connecting the centers of the rings. For hexachiral cells the auxetic property of the lattice together with the elastic coupling modulus between the normal and the asymmetric strains is obtained; a property that has been confirmed here for the tetrachiral lattice. Unlike the hexagonal lattice, the classical constitutive equations of the tetragonal lattice turns out to be characterized by the coupling between the normal and shear strains through an elastic modulus that is an odd function of the parameter of chirality. Moreover, this lattice is found to exhibit a remarkable variability of the Young’s modulus and of the Poisson’s ratio with the direction of the applied uniaxial stress. Finally, a simulation of experimental results is carried out.

Wave Propagation in Auxetic Tetrachiral Honeycombs

This paper describes a numerical and experimental investigation on the flexural wave propagation properties of a novel class of negative Poisson’s ratio honeycombs with tetrachiral topology. Tetrachiral honeycombs are structures defined by cylinders connected by four tangent ligaments, leading to a negative Poisson’s ratio (auxetic) behavior in the plane due to combined cylinder rotation and bending of the ribs. A Bloch wave approach is applied to the representative unit cell of the honeycomb to calculate the dispersion characteristics and phase constant surfaces varying the geometric parameters of the unit cell. The modal density of the tetrachiral lattice and of a sandwich panel having the tetrachiral as core is extracted from the integration of the phase constant surfaces, and compared with the experimental ones obtained from measurements using scanning laser vibrometers.

Flatwise buckling optimization of hexachiral and tetrachiral honeycombs

The flatwise compressive behaviour of tetrachiral and hexachiral honeycombs is analysed, using analytical and Finite Element simulations, both with explicit and implicit formulations. The tetrachiral and hexachiral cells are composed by cylinders connected by four and six tangent ligaments respectively. The ligaments act as mixed stiffeners-elastic foundations during flatwise compressive loading, providing different buckling mode shapes during deformation. The models are compared with experimental results obtained using RP-based honeycombs tested according to ASTM C 393-00 and ASTM C365-00.