Auxetic Behavior Research Articles

Lower hardness than strength: The auxetic composite microstructure of limpet tooth.

The limpet tooth is widely recognized as nature's strongest material, with reported strength values up to 6.5 GPa. Recently, microscale auxeticity has been discovered in the leading part of the tooth, providing a possible explanation for this extreme strength. Utilizing micromechanical experiments, we find hardness values in nanoindentation that are lower than the respective strength observed in micropillar compression tests. Using micromechanical modeling, we show that this unique behavior is a result of local tensile strains during indentation, originating from the microscale auxeticity. As the limpet tooth lacks ductility, these tensile strains lead to microdamage in the auxetic regions of the microstructure. Consequently, indentation with a sharp indenter always probes a damaged version of the material, explaining the lower hardness and modulus values gained from nanoindentation. Micropillar tests were found to be mostly insensitive to such microdamage due to the lower applied strain and are therefore the suggested method for characterizing auxetic nanocomposites. STATEMENT OF SIGNIFICANCE: This work explores the micromechanical properties of limpet teeth, nature's strongest biomaterial, using micropillar compression testing and nanoindentation. The limpet tooth microstructure consists of ceramic nanorods embedded in a matrix of amorphous SiO2 and arranged in a pattern that leads to local auxetic behavior. We report lower values for nanoindentation hardness than for compressive strength, a unique behavior usually not achievable in conventional materials. Utilizing micromechanical finite element simulations, we identify the reason for this behavior to be microdamage formation resultant of the auxetic behavior, sharp indenter tip and lack of ductility of the limpet tooth microstructure. This formation of microdamage is not expected in micropillar compression tests due to lower locally imposed strain.

Auxetic Behaviour of Rigid Connected Squares.

The paper presents an analysis of rotating rigid unit (RRU) auxetic structures, the special property of which is negative Poisson's ratio. The crucial features of such modified structures are the well-functioning linkages of the square units at their pivot points. This ensures the stable functioning of such structures in tension or compression. The presented geometrical analysis of these auxetic structures may facilitate their adequate construction and allow one to determine the expected values of their expansion as well as the desired porosity. The results are confirmed based on the behaviour of physical models produced by the assembly of square units. The change in the dimensions of the physical models when moving from a closed to an open position is consistent with the predictions of the geometric models. By modifying the well-known 'rotating squares' model, physical structures with auxetic properties are obtained that can be utilised in industrial conditions, where a simultaneous change of linear dimensions is needed-either in compression or in tension. The assembly method may prove efficient in building such structures, given the abilities of assembly robots to regularly arrange the unit cells in lines and rows and to connect them with rings at the designated positions (evenly spaced perforations). The presented auxetic structures might find their potential application in, e.g., expansion joints or structures in which the porosity is mechanically changed, such as mesoscale structures. The tested structures subjected to high compressive forces buckle when the yield strength of the rigid unit material is exceeded.

Investigation of Auxetic Structural Deformation Behavior of PBAT Polymers Using Process and Finite Element Simulation.

The current work investigates the auxetic tensile deformation behavior of the inversehoneycomb structure with 5 × 5 cells made of biodegradable poly(butylene adipate-coterephthalate) (PBAT). Fused deposition modeling, an additive manufacturing method, was used to produce such specimens. Residual stress (RS) and warpage, more or less, always exist in such specimens due to their layer-by-layer fabrication, i.e., repeated heating and cooling. The RS influences the auxetic deformation behavior, but its measurement is challenging due to its very fine structure. Instead, the finite-element (FE)-based process simulation realized using an ABAQUS plug-in numerically predicts the RS and warpage. The predicted warpage shows a negligibly slight deviation compared to the design topology. This process simulation also provides the temperature evolution of a small-volume material, revealing the effects of local cyclic heating and cooling. The achieved RS serves as the initial condition for the FE model used to investigate the auxetic tensile behavior. With the outcomes from FE calculation without consideration of the RS, the effect of the RS on the deformation behavior is discussed for the global force-displacement curve, the structural Poisson's ratio evolution, the deformed structural status, the stress distribution, and the evolution, where the first three and the warpage are also compared with the experimental results. Furthermore, the FE simulation can easily provide the global stress-strain flow curve with the total stress calculated from the elemental stresses.

Poisson’s ratio influence on structural dynamic properties of 3D printed bio-based sandwich with an anti-trichiral core

The main interest of this study is to analyze the effect of Poisson’s ratio (negative for auxetic materials) on the dynamic behavior of anti-trichiral structures: an experimental and numerical study is proposed. Using three-dimensional printing technology, anti-trichiral structures (cores and sandwiches) with different geometric parameters were produced with a bio-based composite material. The material used was polylactic acid (PLA) with flax fibers. The structure geometry (anti-trichiral) is the main factor that has an influence in determining its auxetic behavior. In this study, we show the effect of the elementary cell size of the anti-trichiral structure on the auxetic behavior and its impact on the static and dynamic properties of the materials. Initially, experimental tensile tests were used to establish the static characteristics of all specimens, including Poisson’s ratio values. From these results concerning Poisson’s ratios, experimental vibration tests were also carried out to determine their dynamic properties and this is to understand the field of application of these structures and to analyze their behavior in practical use. To validate experimental results, finite element studies were carried out. In this study of the dynamic properties, we observe close agreement convergence between the results of the experimental tests and the numerical analysis.

Quasi-static and dynamic properties studies of a metamaterial with enhanced auxeticity and tunable stiffness

Auxetic metamaterials as a cutting-edge field have attracted extensive attention from researchers because of their peculiar deformation mode and excellent mechanical properties. However, the unstable deformation and low stiffness of auxetic structure limit their potential development. To address these limitations, a novel auxetic honeycomb (NAH) has been proposed by combining an original re-entrant hexagonal honeycomb (RH) with cross-chiral honeycomb (CH). The proposed structure has higher stiffness than RH, and more stability than CH. Additionally, the stiffness, densification point, and auxetic behavior can be adjusted by the angle of cell ribs (θ). In this study, the static mechanical properties and deformation behavior of NAH are investigated experimentally and numerically. Furthermore, the energy absorption and deformation behavior of NAH under different impact loadings (low-, medium- and high-velocity) are investigated numerically. Finally, a series of functionally graded NAHs with varying thicknesses are studied to improve the impact resistance of NAH. The results show that NAH has better specific energy absorption than RH and CH under static compression. Moreover, NAH with θ<90° exhibits greater energy absorption capacity compared to NAH with “θ > 90°” at high-velocity impacts.

Auxetic behavior of 3D-printed structure made in acrylonitrile butadiene styrene and carbon fiber-reinforced polyamide

AbstractParts with an auxetic structure, which exhibit negative Poisson’s ratio, can be associated with a novel class of smart materials. Such interesting property has been widely explored, over the time, for different applications, i.e., medical, automotive, robotic and aeronautic field. However, the research about the design and analysis of auxetic behavior is still on the way. In this paper, a 2D re-entrant honeycomb structure was realized using material extrusion additive manufacturing technology. Two different materials, acrylonitrile butadiene styrene and carbon fiber-reinforced polyamide were adopted. The technique of digital image correlation was implemented during the tensile test to evaluate over the time and in different areas of specimens the strain behavior of the auxetic structure for both investigated materials. The measured negative Poisson’s ratio confirmed the auxetic behavior of the designed structure. The comparison between the two investigated materials showed a different trend of negative Poisson’s ratio.

Design of Mechanical Auxetic Metamaterial for Heterogeneous Assembly, Programmable Periodic Porous Elastomer Structures

With the development of metamaterials, programmable and assembled auxetic structures have attracted extensive attention due to their unusual mechanical behaviors. In this study, we design a 3D printed metamaterial structure with significantly improved stress and programmable auxetic behavior by means of the cooperativity of viscoelastic and elastic materials. The effects of porosity, temperature, the shape of pore and Young’s modulus of the elastic material on the mechanical behavior of 3D printed metamaterial have been characterized using finite element method (FEM) analysis and experimental measurements. The constitutive relationships between stress, strain, porosity and the shape of pore have been formulated to explore the working principles of these parameters in the mechanical performances.

Sine-based lattice plates: additive manufacturing and their mechanical properties when loaded out of plane

PurposeDemanding applications could benefit from the mathematical parametrization of lattice structures as this could lead not only to the characterization of structure–property relation but also facilitates the tailoring of the effective mechanical properties. This paper aims to characterize the mechanical performance of sine-based lattices. The characterization includes the results of in-plane Poisson’s ratio plates models, and the stiffness of additively manufactured lattice plates when loaded in the out-of-plane direction, with the objective of obtaining a relation with their geometrical parameters.Design/methodology/approachThe geometrical parameter–Poisson’s ratio relationship was characterized via finite element (FE) simulations. The stiffness was also measured on additively manufactured polylactic acid lattice plates and contrasted with FE computations.FindingsThe characterization of auxetic lattice plates performed using in-plane and out-of-plane loading leads to key properties when deciding the geometry specific for applications: relative density, auxetic behavior and stiffness. Approximately 26% reduction of stiffness was observed between the square lattice and sine-based lattices of the same volume fraction.Originality/valueAuxetic metamaterials are potential candidates for applications in biomedical engineering, smart sensors, sports and soft robotics. This paper aims to contribute to the existing gap in the study of auxetic metamaterials subjected to complex loading conditions, other than simple tension and compression, required for the mentioned applications.

Bending performance of 3D re-entrant and hexagonal metamaterials

Auxetic structures have theoretically superior bending resistance that was previously inaccessible. Compared with the planar two-dimensional (2D) auxetic structures, the three-dimensional (3D) counterparts may exhibit auxetic behavior in multiple directions. Recently, increasing studies have been devoted to studying the mechanical properties of 3D auxetic structures. In this paper, two 3D honeycomb structures were proposed, namely 3D re-entrant honeycomb and 3D hexagonal honeycomb. Subsequently, the mechanical properties, deformation modes, and deformation mechanisms of these two honeycomb structures under three-point bending were investigated experimentally and numerically. Compared with the 3D non-auxetic hexagonal honeycomb, the 3D auxetic re-entrant honeycomb exhibits higher ductility and fracture resistance. In addition, unlike the conventional honeycomb structure, the mid-span section of the 3D auxetic honeycomb exhibits a trapezoidal deformation mode under bending. Finally, the influence of the number of unit cells and geometric parameters on the mechanical properties of the 3D honeycomb structure were systematically studied by parametric analysis. The excellent bending performance provides a basis for the application of auxetic honeycomb in the fields of biomedicine, soft robots, and buffer devices.

Analytical relationships for 2D Re-entrant auxetic metamaterials: An application to 3D printing flexible implants

Both 2D and 3D re-entrant designs are among the well-known prevalent auxetic structures exhibiting negative Poisson's ratio. The present study introduces novel analytical relationships for 2D re-entrant hexagonal honeycombs for both negative and positive ranges of the cell interior angle θ (θ<0 showing a negative Poisson's ratio). The derived analytical solutions are validated against finite element method (FEM) and experimental results. The results show that, compared to the analytical solutions available in the literature, the analytical relationships presented in this study provide the most accurate results for elastic modulus, Poisson's ratio, and yield stress. The analytical/computational tools are then implemented for designing Kinesio taping (KT) structures applicable to treatment of Achilles tendon injuries. One of the main features of the Achilles tendon is a natural auxetic behavior. Poisson's ratio distribution of an Achilles tendon is obtained using longitudinal and transverse strains and are then used to design and 3D print thermoplastic polyurethane (TPU) KT structures with non-uniform distribution of auxetic unit cells. The presented novel KT shows that it is capable of replicating the deformation and global and local Poisson's ratio distributions, similar to those of the Achilles tendon. Due to the absence of similar formulations and procedures in the literature, the results are expected to be instrumental for designing and 3D printing of flexible implants with unusual auxeticity.

Buckletronics: how compression-induced buckling affects the mechanical and electronic properties of sp2-based two-dimensional materials.

We explore the mechanical and electronic response of sp2-based two-dimensional materials under in-plane compression employing first principles density functional theory-based calculations. Taking two carbon-based graphynes (α-graphyne and γ-graphyne) as example systems, we show that the structures of both two-dimensional materials are susceptible to out-of-plane buckling, which emerges for modest in-plane biaxial compression (1.5-2%). Out-of-plane buckling is found to be more energetically stable than in-plane scaling/distortion and significantly lowers the in-plane stiffness of both graphenes. The buckling also gives rise to in-plane auxetic behaviour in both two-dimensional materials. Under compression, the induced in-plane distortions and out-of-plane buckling also lead to modulations of the electronic band gap. Our work highlights the possibility of using in-plane compression to induce out-of-plane buckling in, otherwise planar, sp2-based two-dimensional materials (e.g. graphynes, graphdiynes). We suggest that controllable compression-induced buckling in planar two-dimensional materials (as opposed to two-dimensional materials, which are buckled due to sp3 hybridization) could provide a route to a new 'buckletronics' approach for tuning the mechanical and electronic properties of sp2-based systems. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

A finite element analysis of auxetic composite fabric with rotating square structure

The auxetic property of macro-porous rotating square structure has been investigated by many using either experimental or numerical approaches. Given the low breaking strength of the typical rotating square structure, it was proposed to employ an elastic base material to the cellular auxetic structure to improve its strength while maintaining its auxetic behavior in our previous study. Despite the experimental studies conducted, a numerical analysis is needed to explain the auxetic effect found in the produced laminated fabrics. In this paper, the auxetic properties of the 2-layer laminated system were simulated using the finite element approach and the effects of the modulus difference between the frame and the base were discussed. The main findings are (1) the simulated results based on a simplified model are broadly consistent with experimental ones under low tensile strain ranges; (2) the initial modulus of the frame material in the stretched direction and that of the base material in the lateral direction are critical to the generation of auxetic effect in the laminated system; (3) at least a 10-time difference of the modulus between the frame and the base materials is required to generate an auxetic effect in the 2-layer laminated structure and the overall auxetic property is increased by enlarging difference of the modulus within a tolerance. It is expected that this research could provide an instructive reference for the future design of auxetic materials.

Sensors Based on Auxetic Materials and Structures: A Review.

Auxetic materials exhibit a negative Poisson's ratio under tension or compression, and such counter-intuitive behavior leads to enhanced mechanical properties such as shear resistance, impact resistance, and shape adaptability. Auxetic materials with these excellent properties show great potential applications in personal protection, medical health, sensing equipment, and other fields. However, there are still many limitations in them, from laboratory research to real applications. There have been many reported studies applying auxetic materials or structures to the development of sensing devices in anticipation of improving sensitivity. This review mainly focuses on the use of auxetic materials or auxetic structures in sensors, providing a broad review of auxetic-based sensing devices. The material selection, structure design, preparation method, sensing mechanism, and sensing performance are introduced. In addition, we explore the relationship between the auxetic mechanism and the sensing performance and summarize how the auxetic behavior enhances the sensitivity. Furthermore, potential applications of sensors based on the auxetic mechanism are discussed, and the remaining challenges and future research directions are suggested. This review may help to promote further research and application of auxetic sensing devices.

GAM: General Auxetic Metamaterial with Tunable 3D Auxetic Behavior Using the Same Unit Cell Boundary Connectivity.

Research on auxetic metamaterials is important due to their high performance against impact loadings and their usefulness in actuators, among other applications. These metamaterials offer a negative Poisson's ratio at the macro level. However, usual auxetic metamaterials face challenges in (1) grading the effect, (2) coupling and combining auxetic metamaterials with non-auxetic materials due to boundary compatibility, (3) obtaining the same auxetic behavior in all directions in the transverse plane, and (4) adapting the regular geometry to the component design boundary and shape. The goal of this paper is to present a novel, recently patented tunable 3D metamaterial created to reproduce a wide spectrum of 3D auxetic and non-auxetic Poisson's ratios and Young's moduli. This wide range is obtained using the same basic unit cell geometry and boundary connections with neighboring cells, facilitating designs using functionally graded metamaterials as only the connectivity and position of the cell's internal nodes are modified. Based on simple spatial triangularization, the metamaterial is easily scalable and better accommodates spatial curvatures or boundaries by changing the locations of nodes and lengths of bars.

Design of isotropic 2D chiral metamaterials based on monohedral pentagonal tessellations

A novel class of transversely-isotropic metamaterials with the potential to exhibit a wide range of Poisson’s ratios and stiffnesses is proposed in this work. These metamaterials, which also have the potential to exhibit auxetic behaviour, are formed through the chiralisation of 2D monohedral Euclidean pentagonal tessellations. Through Finite Element simulations and experimental testing on additively manufactured prototypes, we show that these systems can exhibit Poisson’s ratios which encompass the entire range of transverse isotropicity, i.e. +1 to -1, and that the mechanical properties of these structures can be tailored considerably through variation of the geometric parameters without a loss of global symmetry and isotropy. The level of versatility observed in these new metamaterials exceeds by far that which is commonly found in traditional and well-known isotropic auxetic systems such as hexachiral honeycombs. In addition, analytical expressions pertaining to the geometric limits which define the realisability of this new class of auxetic metamaterials have also been derived and presented. The findings of this work demonstrate that pentagonal tessellations have considerable potential for the development of novel metamaterials and that the geometric constraints associated with transverse isotropy need not necessarily be an insurmountable barrier for the design of metamaterials with tailorable and versatile mechanical properties.

Deformation Behavior Investigation of Auxetic Structure Made of Poly(butylene adipate-co-terephthalate) Biopolymers Using Finite Element Method.

Auxetic structures made of biodegradable polymers are favorable for industrial and daily life applications. In this work, poly(butylene adipate-co-terephthalate) (PBAT) is chosen for the study of the deformation behavior of an inverse-honeycomb auxetic structure manufactured using the fused filament fabrication. The study focus is on auxetic behavior. One characteristic of polymer deformation prediction using finite element (FE) simulation is that no sounded FE model exists, due to the significantly different behavior of polymers under loading. The deformation behavior prediction of auxetic structures made of polymers poses more challenges, due to the coupled influences of material and topology on the overall behavior. Our work presents a general process to simulate auxetic structural deformation behavior for various polymers, such as PBAT, PLA (polylactic acid), and their blends. The current report emphasizes the first one. Limited by the state of the art, there is no unified regulation for calculating the Poisson's ratio ν for auxetic structures. Here, three calculation ways of ν are presented based on measured data, one of which is found to be suitable to present the auxetic structural behavior. Still, the influence of the auxetic structural topology on the calculated Poisson's ratio value is also discussed, and a suggestion is presented. The numerically predicted force-displacement curve, Poisson's ratio evolution, and the deformed auxetic structural status match the testing results very well. Furthermore, FE simulation results can easily illustrate the stress distribution both statistically and local-topology particularized, which is very helpful in analyzing in-depth the auxetic behavior.

Optimization of the Cross-Sectional Geometry of Auxetic Dowels for Furniture Joints

In this study, the aim was to optimize the cross-sectional geometry of auxetic dowels for furniture joints. For this purpose, two different sizes of auxetic dowels were chosen, one for frame- and the other for panel-type furniture joints for designing the cross-sectional geometry. Auxetic patterns that are created on the cross-sectional area cause deficiency of the materials, and this phenomenon decreases the modulus of elasticity (MOE) and increases the member stress. Accordingly, maximum MOE values and minimum Poisson's ratio levels were determined for the optimum strength-auxetic behavior relation by means of a Monte Carlo method. Furthermore, Poisson's ratio of the optimized dowel's cross-section was confirmed with experimental tests, numerical analyses and analytical calculations. As a result, Poisson's ratio values were obtained as negative values and confirmed, which means the dowels designed in this study had auxetic behavior. In conclusion, it could be said that studies should be conducted on the performance of auxetic dowels in both frame and panel furniture joints.

Variant design generation and machine learning aided deformation prediction for auxetic metamaterials

Auxetic metamaterials have been applied in many domains due to their unique auxetic behavior, tunable local kinematics, and morphological intelligence. However, the classic auxetic designs normally cannot be directly applied due to their defects. How to modify the existing classic design to achieve diverse but also valid variant designs remains a challenging problem. One common approach is to use predefined parameters and fine-tune these parameters. Yet, this approach limits the design space and highly relies on expert knowledge. In this paper, we proposed a variant design generation method based on a path-finding algorithm to achieve pixel-level design freedom. Meanwhile, to support the evaluation of designs in such a large design space, we developed a multi-scale geometry-informed Graph U-net. More specifically, we proposed MeshPool—a predefined clustering-based pooling technique, and distortion loss—a geometry-informed loss function inspired by finite element analysis (FEA). A variant design family for re-entrant structures is generated as a case study to validate the variant design generation method. And the Graph U-net is developed to predict complex nonlinear deformation with simple linear FEA results. The results from the case study demonstrated that the proposed variant design generation method covered the properties space of re-entrant structures and the developed Graph U-net achieved accurate prediction with a nodal displacement mean absolute error (MAE) of around 0.0169 mm under an average nodal displacement of 0.5058 mm. More importantly, we demonstrated the graph neural network’s unique capability of learning gradient information compared with convolutional neural network in a benchmark on strain and stress.

Unusual mechanical properties of CO2–V: Auxetic potential in a high-pressure polymorph of carbon dioxide

In this work, the structural, mechanical, and vibrational properties of CO2–V have been investigated by employing first-principles DFT calculations. It is shown, for the first time, that the CO2–V single crystal has the potential to exhibit a negative Poisson's ratio for loading in all directions in the (001) plane in the pressure range 40–60 GPa. It is also shown that the Poisson's ratio of CO2–V is pressure-dependent, with an increase in pressure resulting in an increase in the auxetic potential of the system. The auxetic behaviour of this system has been analysed by studying its deformation under the application of stress through both two-dimensional and three-dimensional approaches. From a two-dimensional perspective, the auxeticity of CO2–V can be explained by the relative rotation of semi-rigid projected squares, which both rotate and deform upon application of a stress. As the hydrostatic pressure is increased, the rigidity of the units increases, resulting in less deformation of the squares and hence an increase in auxetic potential. From a three-dimensional perspective, the auxetic behaviour of CO2–V can be rationalised in terms of the interplay between relative rotation of CO4 tetrahedra, coupled with stretching and deformation of these CO4 units. All of this is very significant, as it enhances the corpus of knowledge on the mechanical properties of a high-pressure polymorph of CO2, a substance that plays a significant role in planetary science.

Shape Memory Alloy Thin Film Auxetic Structures

AbstractAuxetic structures provide an interesting approach to solving engineering problems due to their negative Poisson's ratio, which allows for elongation perpendicular to applied stresses, opposite to a conventional structure's necking behavior. Thus, they can function well in applications requiring compacting the device into a small volume during the deployment (e.g., implants inserted with catheters) or stretchability with area coverage (e.g., stretchable electronics). Fabricating them with shape memory alloys (SMAs) expands the possibilities. The high strains experienced by auxetic structures may become reversible compared to ordinary metals due to superelastic or shape memory effect. This work studies four different auxetic microstructures using thin film SMAs that are capable of surviving strains up to 57.4%. Since these structures are fabricated by layer deposition and lithography, other components, such as microelectronics, can be seamlessly integrated into the fabrication process. These auxetic thin films are investigated for their mechanical behavior under tension for their stretchability and stability. Under tension, thin films are known to show wrinkling instabilities. In two of four designs, the large auxetic behavior leads to wrinkling, while the other two display stable, non‐wrinkling behavior. These designs can be candidates for stretchable electronics, wearable medical devices (e.g., biosensors), or implants (e.g., stents).