Controllable Hierarchical Mechanical Metamaterials Guided by the Hinge Design

In this work, we use computer simulations (Molecular Dynamics) to analyse the behaviour of a specific auxetic hierarchical mechanical metamaterial composed of square-like elements. We show that, depending on the design of hinges connecting structural elements, the system can exhibit a controllable behaviour where different hierarchical levels can deform to the desired extent. We also show that the use of different hinges within the same structure can enhance the control over its deformation and mechanical properties, whose results can be applied to other mechanical metamaterials. In addition, we analyse the effect of the size of the system as well as the variation in the stiffness of its hinges on the range of the exhibited auxetic behaviour (negative Poisson’s ratio). Finally, it is discussed that the concept presented in this work can be used amongst others in the design of highly efficient protective devices capable of adjusting their response to a specific application.     

Design,Manufacture, and Characterization of Auxetic Yarns with Multiple Core/Wrap Structure by Braiding Method

Auxetic textiles with a negative Poisson’s ratio show significant energy absorption and synclastic curvature characteristics and potential application value in sportsmen protection material. The stability and reliability of the structure and properties of auxetic textiles is also an important factor to assess and promote the application. Thus, auxetic yarns with multiple core/wrap structure were prepared by a 16-spindle braiding machine. It mainly focused on the axial stretching behavior and the relationship between the structure and auxetic effect of yarn samples. The maximum Poisson’s ratio of auxetic yarns was −3.26. The experimental results also showed that the complex yarns still presented an auxetic effect during 30 repeats of cycle stretching. According to the study about the repeatable stretchability and auxetic effect of complex yarns, it could be expected to provide more comfortable, safer, and smarter protective textiles.     

Inversion Method of the Young’s Modulus Field and Poisson’s Ratio Field for Rock and Its Test Application

As one typical heterogeneous material, the heterogeneity of rock micro parameters has an important effect on its macro mechanical behavior. The study of the heterogeneity of micro parameters is more important to reveal the root cause of deformation and failure. However, as a typical heterogeneous material, the current testing and inversion method is not suitable for micro parameters measurement for the rock. Aiming at obtaining the distribution of micro Young’s modulus and micro Poisson’s ratio of the rock, based on the digital image correlation method (DIC) and finite element method (FEM), this paper proposed a parameter field inversion method, namely the DF-PF inversion method. Its inversion accuracy is verified using numerical simulation and laboratory uniaxial compression test. Considering the influences of heterogeneity, stress state and dimension difference, the average inversion error of Young’s modulus field and Poisson’s ratio field are below 10%, and the proportion of elements with an error of less than 15% accounts for more than 86% in the whole specimen model. Compared with the conventional measuring method, the error of macro Young’s modulus and macro Poisson’s ratio calculated by the DF-PF inversion method is less than 2.8% and 9.07%, respectively. Based on the statistical analysis of Young’s modulus field and Poisson’s ratio field, the parameter homogeneity and quantitative function relation between the micro parameter and the principal strain can also be obtained in laboratory tests. The DF-PF inversion method provides a new effective method of testing Young’s modulus field and Poisson’s ratio field of the rocks under complex stress states.     

Mechanical Parameters of Leather in Relation to Technological Processing of the Footwear Uppers

This paper aimed to define two critical mechanical properties of leather—Young’s modulus and Poisson ratio—essential to the virtual simulation of the behaviour of the footwear uppers against the manufacturing operations of stitching and perforating. The following technological aspects were considered to analyse the materials from manufacturing conditions point of view: the number of layers (one layer and two layers), the nature of the materials used for uppers subgroups (calfskin-outer upper, sheep leather-lining, polyester knitted fabric-lining), the overlapping width in the stitching area, the number of parallel stitches (single stitch and double stitch), the punching interval and the type of perforations (simple and with eyelets), resulting in nine kinds of samples. Furthermore, the elasticity (Young’s modulus) and lateral contraction (Poisson’s ratio) were calculated during the tensile strength analysis performed on the SATRA STM 466 equipment. Both mechanical parameters are essential to simulate the behaviour of the virtual footwear prototypes in various conditions.     

Study on a Chiral Structure with Tunable Poisson’s Ratio

A chiral structure with a negative Poisson’s ratio containing a hollow circle with varying diameters was designed, and the finite element method was used to investigate the variation in the Poisson’s ratio when the hollow circle diameter was varied (d = 0, 1, 2, 3, and 4 mm). The simulation results showed that the Poisson’s ratio was sensitive to the hollow circle diameter, and the minimum Poisson’s ratio was −0.43. Three specimens with different hollow circle diameters (d′ = 0, 1, and 3 mm) were 3D-printed from thermoplastic polyurethane, and the Poisson’s ratio and equivalent elastic modulus were measured. In the elastic range, the Poisson’s ratio increased and the equivalent elastic modulus decreased as the hollow circle diameter increased. The simulation and experimental results showed good agreement. The proposed structure is expected to be applicable to protective sports gear owing to its high energy absorption and the fact that its properties can be modified as required by adjusting the geometric parameters of the unit cell.     

Re-Entrant Honeycomb Auxetic Structure with Enhanced Directional Properties

This paper presents a modified re-entrant honeycomb auxetic structure. The structure is constructed by adding an additional horizontal member between the vertical and re-entrant member of the semi-re-entrant honeycomb model to increase the overall compliance of the structure in order to obtain higher values of negative Poisson’s ratio (NPR). An analytical model of the structure is presented, taking into account the bending, shear, and axial deformations. The model is verified using finite element analysis (FEA) and tensile testing. The results of FEA and tensile testing corroborate the results of the presented mathematical model. The structure is also compared to the existing re-entrant honeycomb structure. The newly added strut has shown a direct effect on the directional properties of the overall structure. With an increase in the newly added strut to re-entrant lengths, NPR was significantly enhanced in the x-direction and reduced in the y-direction loadings. The structure shows an improved Young’s modulus compared to solid material in both loading directions, especially for the low values of the new strut and re-entrant lengths ratio. The structure also shows that high NPR can be achieved for low relative density compared to semi re-entrant honeycomb structure.     

Investigation of Modified Auxetic Structures from Rigid Rotating Squares

Auxetic structures exhibit unusual changes in size, expanding laterally upon stretching instead of contracting. This paper presents this effect in a failsafe mode in structures made of rigid squares. We applied the concept of auxetic structures made of rigid rotating squares (from Grima and Evans) and offer a novel solution for connecting them. By introducing axes of rotation on the surface of the squares, a reliable working system is obtained, free from stress, in which the squares can come into contact with each other and completely cover the surface of the structure, or, in the open position, form regularly arranged pores. Herein, we present a new 2D auxetic metamaterial that is mathematically generated based on a theoretical relationship of the angle between the edges of a square and the position of the axis of rotation. Physical models were generated in the form of a planar structure and in the form of a circular closed structure. Such physical models confirmed our initial considerations and the geometrical relationships, offering new application possibilities. The novel structure that was designed and manufactured for the purpose of the paper can be considered as a new proposal in the market of auxetic materials.     

Evaluation of the Equivalent Mechanical Properties of Lattice Structures Based on the Finite Element Method

Lattice structures have excellent mechanical properties and can be designed by changing the cellular structure. However, the computing scale is extremely large to directly analyze a large-size structure containing a huge number of lattice cells. Evaluating the equivalent mechanical properties instead of the complex geometry of such lattice cells is a feasible way to deal with this problem. This paper aims to propose a series of formulas, including critical structural and material parameters, to fast evaluate the equivalent mechanical properties of lattice structures. A reduced-order model based on the finite element method and beam theory was developed and verified by comparing it with the corresponding full model. This model was then applied to evaluate the equivalent mechanical properties of 25 types of lattice cells. The effects of the material Young’s modulus and Poisson’s ratio, strut diameter, cell size, and cell number on those equivalent mechanical properties were investigated and discussed, and the linear relationship with the material parameters and the non-linear relationship with the structural parameters were found. Finally, a series of analytical-fitting formulas involving the structural and material parameters were obtained, which allows us to fast predict the equivalent mechanical properties of the lattice cells.     

Study on the Tensile Behavior of Helical Auxetic Yarns with Finite Element Method

Complex yarns with helical wrapping structure show auxetic effect under axial tension and a wide perspective application. Experimental results suggested that initial helical angle was one of the most important structural parameters. However, the experimental method was limited and could not effectively explain the deformation behavior or auxetic mechanism. A finite element model of the helical auxetic yarn was built and used to analyze the interactive relationship between the two components and the stress distribution mode. The effectiveness and accuracy of the model was first verified by comparing with the experimental results. The simulation results showed that the complex yarn with initial helical angle of 14.5° presented the maximum negative Poisson’s ratio of −2.5 under 5.0% axial strain. Both the contact property between the two components and the radial deformability of the elastic core filament were key factors of the auxetic property. When the contact surfaces were completely smooth and the friction coefficient μ was set to 0, the complex yarn presented non-auxetic behavior. When the Poisson’s ratio of the core filament was 0, the complex yarn showed greater auxetic effect. During the axial stretching, the tensile stress was mainly distributed in the wrap filament, which led to structural deformation and auxetic behavior. A pair of auxetic yarns showed pore effect and high expansion under axial strain. Thus, it may be necessary to consider new weaving structures and preparation methods to obtain the desired auxetic property and application of auxetic yarns.     

Setting Times of Early-Age Mortars Determined from Evolution Curves of Poisson’s Ratio

Setting times, as the early-age properties of cement-based materials, are important properties to ensure the quality and long-term performance of engineering structures. To determine the initial and final setting times of cementitious materials, the compressive wave velocity and shear wave velocity of six early-age mortar samples were monitored. Their time evolution curves of Young’s modulus, shear modulus, bulk modulus, and Poisson’s ratio were then calculated and analyzed. The signature times of the derivatives of the Poisson’s ratio evolution curves correlate well with the initial and final setting times, and the remarkably high coefficient of determination values relative to the data from this study are higher than those presented in the current literature. The proposed derivative method on the Poisson’s ratio evolution curve is as good as the derivative methods from vs. evolution curves used by prior studies for the estimation of both the initial and final setting times of the early-age properties of cement-based materials. The formation and subsequent disappearance of ettringite of low Poisson’s ratio were postulated to cause the initial dip in the Poisson’s ratio evolution curves.     

Chirality-Dependent and Intrinsic Auxeticity for Single-Walled Carbon Nanotubes

Single-walled carbon nanotubes (SWCNTs) have superior mechanical properties which originate from a strong C-C covalent bond and unique nanostructure. Chirality, one of the helical structural parameters of SWCNTs, leads to differences in mechanical performance. In this work, molecular dynamics (MD) simulation was performed to analyze engineering Poisson’s ratio (EPR) and incremental Poisson’s ratio (IPR) of SWCNTs with different chiral angles, respectively, under tensile and compressive load, as well as the chiral effect on rigidity. We reported the minimum EPR for (4, 1) SWCNT and obtained the distribution and trend of EPR which is dependent on chiral index m. In addition, a new observation showed two exactly opposite trends of EPR existing not only in tension and compression but also in the longitudinal and radial directions. Furthermore, we found that the critical strain, over which SWCNT would be auxetic, ranged from 6% to 18% and was also chirality-dependent. Three representative SWCNTs with chiral angle of 0° (zigzag), 10.89° (chiral), and 30° (armchair) were selected for the mechanism study of auxeticity. Finally, a method of the contribution to radial strain for two main deformation modes proposed in this paper could well explain the negative IPR phenomenon.     

An Experimental Study of Auxetic Tubular Structures

Auxetic tubular structures are widely known structures, characterized by a negative Poisson’s ratio upon stretching and deformation in the axial and transverse directions, which have numerous application possibilities. In this paper, tubular structures were realized by rolling up planar auxetic structures and using rigid square frames as unit cells. Planar and tubular structures were built from square frames that were 3D printed with plastic or laser-cut from metal. The changes in linear dimensions of the studied structures were based on a hinge mechanism, the functioning of which was experimentally verified on different solutions leading to square unit cells. To connect the square frames of the structure, an innovative solution was used in the form of rotation axes on their surface at a preset distance from the edge of the square frame. The geometric parameter thus introduced was used to determine the relative change in the size of the structure when stretched (i.e., when moving from the closed to the open position).     

Applicability of Pre-Plastic Deformation Method for Improving Mechanical Properties of Bulk Metallic Glasses

Pre-plastic deformation (PPD) treatments on bulk metallic glasses (BMGs) have previously been shown to be helpful in producing multiple shear bands. In this work, the applicability of the PPD approach on BMGs with different Poisson’s ratios was validated based on experimental and simulation observations. It was found that for BMGs with high Poisson’s ratios (HBMGs, e.g., Zr₅₆Co₂₈Al₁₆ and Zr₄₆Cu₄₆Al₈), the PPD treatment can easily trigger a pair of large plastic deformation zones consisting of multiple shear bands. These PPD-treated HBMGs clearly display improved strength and compressive plasticity. On the other hand, the mechanical properties of BMGs with low Poisson’s ratios (LBMG, e.g., Fe₄₈Cr₁₅Mo₁₄Y₂C₁₅B₆) become worse due to a few shear bands and micro-cracks in extremely small plastic deformation zones. Additionally, for the PPD-treated HBMGs with similar high Poisson’s ratios, the Zr₅₆Co₂₈Al₁₆ BMG exhibits much larger plasticity than the Zr₄₆Cu₄₆Al₈ BMG. This phenomenon is mainly due to more defective icosahedral clusters in the Zr₅₆Co₂₈Al₁₆ BMG, which can serve as nucleation sites for shear transformation zones (STZs) during subsequent deformation. The present study may provide a basis for understanding the plastic deformation mechanism of BMGs.     

Removing Auxetic Properties in f.c.c. Hard Sphere Crystals by Orthogonal Nanochannels with Hard Spheres of Another Diameter

Negative Poisson’s ratio materials (called auxetics) reshape our centuries-long understanding of the elastic properties of materials. Their vast set of potential applications drives us to search for auxetic properties in real systems and to create new materials with those properties. One of the ways to achieve the latter is to modify the elastic properties of existing materials. Studying the impact of inclusions in a crystalline lattice on macroscopic elastic properties is one of such possibilities. This article presents computer studies of elastic properties of f.c.c. hard sphere crystals with structural modifications. The studies were performed with numerical methods, using Monte Carlo simulations. Inclusions take the form of periodic arrays of nanochannels filled by hard spheres of another diameter. The resulting system is made up of two types of particles that differ in size. Two different layouts of mutually orthogonal nanochannels are considered. It is shown that with careful choice of inclusions, not only can one impact elastic properties by eliminating auxetic properties while maintaining the effective cubic symmetry, but also one can control the anisotropy of the cubic system.     

Elastic Properties and Hardness of Mixed Alkaline Earth Silicate Oxynitride Glasses

The incorporation of nitrogen as a second anion species into oxide glasses offers unique opportunities for modifying glass properties via changes in glass polymerization and structure. In this work, the compositional dependence of elastic properties and the nanoindentation hardness of mixed alkaline-earth silicate oxynitride glasses containing a high amount of nitrogen (>15 at.%, c.a. 35 e/o) were investigated. Three series of silicon oxynitride glass compositions AE–Ca–Si–O–N glasses (where AE = Mg, Sr, and Ba) having varying amounts of modifiers were prepared using a new glass synthesis route, in which a precursor powder of metal hydrides was used. The obtained glasses contained high amounts of N (19 at.%, c.a. 43 e/o) and modifier cations (26 at.%, c.a. 39 e/o). Mg–Ca–Si–O–N glasses had high values of nanohardness (12–16 GPa), along with a reduced elastic modulus (130–153 GPa) and Young’s modulus (127–146 GPa), in comparison with the Sr–Ca- and Ba–Ca-bearing oxynitride glasses. Both the elastic modulus and the nanohardness of AE–Ca–Si–O–N glasses decreased with an increase in the atomic number of the AE element. These property changes followed a linear dependence on the effective cation field strength (ECFS) of the alkaline earth (AE) modifier, according to their valences and ionic radii. No mixed alkaline-earth effect was observed in the current investigation, indicating that the properties were more dictated by the nitrogen content.     

Ultrasonic Assessment of the Influence of Cold Rolling and Recrystallization Annealing on the Elastic Constants in a TWIP Steel

The evolution of the elastic constants, C33, C44 and C55, Poisson’s ratio and acoustic birefringence of a Fe-0.5 wt% C-21.5 wt% Mn twinning-induced plasticity (TWIP) steel with reduction by cold rolling and recrystallization annealing was assessed from measurements of the times of flight of ultrasonic waves propagating along the thickness of the rolled plates. As the reduction increased, changes in the elastic constants resulted in a steadily increasing orthotropy, which was clearly shown by Poisson’s ratio and acoustic birefringence. Although optical metallography and hardness measurements showed that partial or full recrystallization is attained after annealing at 600 °C and 700 °C, the ultrasonic measurements revealed that a high level of orthotropy remains.     

Investigating the Effective Performance of Sandwich Panel with Petal Star-Triangular Core Using VAM-Based Equivalent Model

On the basis of star-shaped core sandwich panel, a novel sandwich panel with petal-triangle core (SP-PSC) was proposed to improve the negative Poisson’s ratio (NPR) effect while retaining the characteristics of light weight and high strength. To study the complex structure more conveniently and quickly, a variational asymptotic method-based equivalent two-dimensional model (2D-EPM) was developed. The accuracy and efficiency of 2D-EPM were verified by the three-point bending experiment data and the 3D FE model results under different boundary and load conditions. The effects of the geometric parameters on the equivalent stiffness, buckling, natural frequency and NPR effect were also investigated. To increase the NPR of SP-PSC, the material of facesheet was changed from isotropic material to unidirectional CFPR material, and the influence of the material anisotropy on the NPR effect of SP-PSC was investigated. It is found that the NPR of SP-PSC increased first and then decreased with the increase in the fiber angle, reaching the maximum value at 40–50∘. At the same time, this law is applicable to SP-PSC with different material or geometric parameters. Finally, two improved cores, petal star-triangular core with X-shaped ligaments (PSC-X) and double-arc star-shaped core (DSC), were proposed and compared with SP-PSC in equivalent stiffness and recovered local fields to demonstrate their advantages. Compared with the original plate, the stress concentration and equivalent stiffness of the two improved PSCs significantly improved.     

Idealized 3D Auxetic Mechanical Metamaterial: An Analytical,Numerical, and Experimental Study

Mechanical metamaterials are man-made rationally-designed structures that present unprecedented mechanical properties not found in nature. One of the most well-known mechanical metamaterials is auxetics, which demonstrates negative Poisson’s ratio (NPR) behavior that is very beneficial in several industrial applications. In this study, a specific type of auxetic metamaterial structure namely idealized 3D re-entrant structure is studied analytically, numerically, and experimentally. The noted structure is constructed of three types of struts—one loaded purely axially and two loaded simultaneously flexurally and axially, which are inclined and are spatially defined by angles θ and φ. Analytical relationships for elastic modulus, yield stress, and Poisson’s ratio of the 3D re-entrant unit cell are derived based on two well-known beam theories namely Euler–Bernoulli and Timoshenko. Moreover, two finite element approaches one based on beam elements and one based on volumetric elements are implemented. Furthermore, several specimens are additively manufactured (3D printed) and tested under compression. The analytical results had good agreement with the experimental results on the one hand and the volumetric finite element model results on the other hand. Moreover, the effect of various geometrical parameters on the mechanical properties of the structure was studied, and the results demonstrated that angle θ (related to tension-dominated struts) has the highest influence on the sign of Poisson’s ratio and its extent, while angle φ (related to compression-dominated struts) has the lowest influence on the Poisson’s ratio. Nevertheless, the compression-dominated struts (defined by angle φ) provide strength and stiffness for the structure. The results also demonstrated that the structure could have zero Poisson’s ratio for a specific range of θ and φ angles. Finally, a lightened 3D re-entrant structure is introduced, and its results are compared to those of the idealized 3D re-entrant structure.     

Cancellation of Auxetic Properties in F.C.C. Hard Sphere Crystals by Hybrid Layer-Channel Nanoinclusions Filled by Hard Spheres of Another Diameter

The elastic properties of f.c.c. hard sphere crystals with periodic arrays of nanoinclusions filled by hard spheres of another diameter are the subject of this paper. It has been shown that a simple modification of the model structure is sufficient to cause very significant changes in its elastic properties. The use of inclusions in the form of joined (mutually orthogonal) layers and channels showed that the resulting tetragonal system exhibited a complete lack of auxetic properties when the inclusion spheres reached sufficiently large diameter. Moreover, it was very surprising that this hybrid inclusion, which can completely eliminate auxeticity, was composed of components that, alone, in these conditions, enhanced the auxeticity either slightly (layer) or strongly (channel). The study was performed with computer simulations using the Monte Carlo method in the isothermal-isobaric (NpT) ensemble with a variable box shape.     

Hierarchical Fibers with a Negative Poisson’s Ratio for Tougher Composites

In this paper, a new kind of hierarchical tube with a negative Poisson’s ratio (NPR) is proposed. The first level tube is constructed by rolling up an auxetic hexagonal honeycomb. Then, the second level tube is produced by substituting the arm of the auxetic sheet with the first level tube and rolling it up. The Nth (N ≥ 1) level tube can be built recursively. Based on the Euler beam theory, the equivalent elastic parameters of the NPR hierarchical tubes under small deformations are derived. Under longitudinal axial tension, instead of shrinking, all levels of the NPR hierarchical tubes expand in the transverse direction. Using these kinds of auxetic tubes as reinforced fibers in composite materials would result in a higher resistance to fiber pullout. Thus, this paper provides a new strategy for the design of fiber reinforced hierarchical bio-inspired composites with a superior pull-out mechanism, strength and toughness. An application with super carbon nanotubes concludes the paper.