Auxetic Behavior Research Articles

Computational screening of 2D ternary penta-materials with auxetic properties and efficient photocatalytic CO2 reduction

Due to unique structural and electronic properties, pentagon-based two-dimensional (2D) materials have captured significant interest in recent years. However, previous studies on these materials have primarily focused on unary and binary systems, with less exploration of ternary pentagonal structures. Herein, we conducted first-principles calculations to evaluate the stability of 122 ternary pentagonal monolayers composed of metals, nitrogen, and chalcogen. We identify six highly stable candidates, including AuNS, CuNTe, GaNS, InNS, SbNS, and SbNSe that meet the criteria for thermodynamic, mechanical, and dynamic stability. Mechanical property analysis reveals that five of these monolayers demonstrate auxetic behavior. Electronic structure calculations show that all candidates are semiconductors with band gaps ranging from 0.12 to 3.42 eV. Specifically, the SbNS and SbNSe monolayers are indirect semiconductors with band gaps of 2.25 and 2.27 eV, respectively. These materials exhibit strong visible light absorption, and potentially serve as exceptional photocatalysts for the reduction of CO2 to CH4 due to the optimal band alignment. The free energy change in the rate-limiting step is even lower than those found in g-C3N4 and MoS2-based systems. Our findings highlight new pentagon-based 2D materials with remarkable electronic, mechanical, and optical properties, making them promising candidates for applications in mechanics and energy conversion.

EXPERIMENTAL ANALYSIS OF POISSON RATIO ON METAMATERIALS MANUFACTURED FROM CRUMPLED ALUMINUM FOIL SUBJECTED TO UNIAXIAL COMPRESSION

In this work experimental results are presented concerning the auxetic behavior of a crumpled metamaterial manufactured with aluminum foil, so far such experimental evidence has not been reported by other authors. Thus, 2D digital image correlation (DIC) was used to make full field measurements of longitudinal and transverse strains on the surface of crumpled aluminum specimens under axial compression; it was no possible to use conventional methods on the measurements of strains, such as strain gages or extensometers, due to the irregular topography on the surface of the specimens. The obtained results exhibit the auxetic nature of the aluminum crumpled material, with Poisson´s ratio values that vary from ?=-0.17 to ?=-0.02 for relative densities in the range ?_r=0.07 to ?_r=0.21. Keywords: Auxetic, Digital Image Correlation, Crumpled material, Poisson, Computer vision system.

Application of machine learning algorithm and Carrera unified formulation in thermal buckling analysis of a functionally graded graphene origami enabled auxetic metamaterial sandwich plate with an auxetic concrete foundation

This study presents a comprehensive thermal buckling analysis of sandwich plates composed of functionally graded graphene origami-enabled auxetic metamaterial (FG-GOEAM) face sheets on an auxetic concrete foundation, using Carrera’s unified formulation (CUF) as the theoretical framework. FG-GOEAM materials are emerging as advanced composites, combining exceptional mechanical resilience, tunable auxetic behavior, and high thermal stability, making them suitable for extreme environments. By employing CUF, a powerful and adaptable modeling approach, this work accurately captures the complex mechanical interactions within the FG-GOEAM sandwich structure under thermal loads, incorporating both material gradation and auxetic properties. To further enhance the precision and efficiency of this thermal buckling analysis, a deep neural network (DNN) is developed as a machine learning algorithm to predict critical temperature differences, based on a dataset generated through mathematics simulation. The DNN model demonstrates excellent predictive capability, validated by close alignment between its estimates and CUF results, thus reducing computational costs while maintaining high accuracy. Parametric studies are conducted to assess the effects of material gradation, aspect ratios, and foundation properties on thermal buckling performance. The results highlight the superior thermal stability of FG-GOEAM structures and the potential of DNNs to serve as reliable, computationally efficient tools for advanced structural analysis. This study provides a novel, integrated framework for high-fidelity thermal buckling prediction in complex auxetic composites, paving the way for broader applications in engineering fields requiring lightweight, thermally stable structures.

Additive manufactured 3D re-entrant auxetic structures for enhanced impact resistance

Abstract This study presents a novel exploration of the geometric parameters within a 3D re-entrant auxetic lattice structure, specifically focusing on their unique impact energy absorption properties, which were systematically evaluated through drop weight impactor testing. Each lattice configuration was additively manufactured using stereolithography, allowing for precise control over strut thickness (t), re-entrant angle (θ), and the aspect ratio (h/l) of unit cells during both low and high energy impact scenarios. This study found that the overall auxetic behavior is predominantly controlled by the aspect ratio of the cell ribs, while the modulus is governed by rib thickness. A finite element model was subsequently developed to simulate the experimental impact loading conditions and was used to examine a wider range of parameters that were not experimentally tested. The simulated dynamic test results displayed the deformation trends and changes to the Poisson's ratio. Among the studied parameters, experimental results highlighted that a lattice structure with t = 1.6 mm, θ = 65°, and a h/l ratio = 1.8 exhibited the highest specific energy absorption (SEA) under uniaxial impact deformation with 5 Joules of impact energy. Conversely, when employing 20 Joules of impact energy revealed the greatest SEA at t = 1.0 mm, θ = 65°, and an h/l ratio of 2.2. The results demonstrate unique deformation mechanism of auxetic structures under impact loading and the capacity to adapt the 3D re-entrant lattice structure for applications requiring tailored impact energy absorption.

Tiling-based lattice generation for structural property exploration

Advancements in additive manufacturing enable the development of artificial lattice structures with unique properties not found in natural materials. Specifically, filament-based lattices are known for having a lightweight yet strong nature, exhibiting auxetic behavior and excellent energy absorption capabilities. Recent research has focused on developing algorithms and frameworks to manipulate cell geometry and material properties to achieve unusual properties. However, the exploration of the full design space is hampered in practice primarily due to restrictions on cell tiling variation. Here, for the first time, a Tiling-Based Lattice Generation (TBLatGen) framework is presented that relies on various tiling operations and stochastic changes in internal cell geometry. By utilizing reflections, rotations, glide reflections, translations, and combinations of these operations, lattice structures are tiled to achieve an extensive range of properties. For instance, achieving Poisson's ratios ranging over at least ±20 using a minimal set of design parameters is demonstrated, a range unprecedented in prior studies. Experimental testing of a physical prototype validates the auxetic behavior of one newly proposed tiled lattice structure. Beyond this, the proposed TBLatGen framework is anticipated to be applicable to general periodic metamaterials, enabling the design and discovery of new structures exhibiting exceptional mechanical, thermal, electrical, or magnetic properties.

Easy-to-use formulations based on the homogenization theory for vascular stent design and mechanical characterization

Background and objectivesVascular stents are scaffolding structures implanted in the vessels of patients with obstructive disease. Stents are typically designed as cylindrical lattice structures characterized by the periodic repetition of unit cells. Their design, including geometry and material characteristics, influences their mechanical performance and, consequently, the clinical outcomes. Computational optimization frameworks have proven to be effective in assisting the design phase of vascular stents, facilitating the achievement of enhanced mechanical performances. However, the reliance on time-consuming simulations and the challenge of automating the design process limit the number of design evaluations and reduce optimization efficiency. In this context, a rapid and automated method for the mechanical characterization of vascular stents is presented, taking the stent geometry, conceived as the periodic repetition of a unit cell, and material as input and providing the mechanical response of the stent as output. MethodsVascular stents were assumed to be thin-walled hollow cylinders sharing the same macroscopic geometrical characteristics as the cylindrical lattice structure but composed of an anisotropic homogenized material. Homogenization theory was applied to average the microscopic inhomogeneities at the stent unit cell level into a homogenized material at the macro-scale, enabling the calculation of the associated homogenized material tensor. Analytical formulations were derived to relate the stent mechanical behavior to the homogenized stiffness tensor, considering linear elastic theory for thin-walled hollow cylinders and three loading scenarios of relevance for vascular stents: radial crimping; axial traction; torsion. Validation was conducted by comparing the derived analytical formulations with results obtained from finite element analyses on typical stent designs. ResultsHomogenized stiffness tensors were computed for the unit cells of three stent designs, revealing insights into their mechanical performance, including whether they exhibit auxetic behavior. The derived analytical formulations were successfully validated with finite element analyses, yielding low relative differences in the computed values of foreshortening, radial, axial and torsional stiffnesses for all three stents. ConclusionsThe proposed method offers a rapid, fully automated procedure that facilitates the assessment of the mechanical behavior of vascular stents and is suitable for effective integration into computational optimization frameworks.

Unlocking Auxetic Behavior in Recyclable Thermosetting Foams Enabled by Dynamic Disulfide Cross‐linking Strategy

AbstractAuxetic foams with a negative Poisson's ratio (NPR) have attracted considerable attention in material engineering due to their outstanding performance in seismic and energy absorption. Nevertheless, thermoplastic auxetic foams are compromised by weak non‐covalent crosslinking that diminishes the mechanical strength and durability of foams. Conversely, thermosetting foams with chemical crosslinking, although mechanically robust, face challenges in elaborating auxetic structure and in achieving recyclability. Herein, an alternative approach is proposed to tackle this dilemma by incorporating dynamic disulfide bonds into the polymer network for preparing a thermosetting polyurethane foam with covalent adaptable network. By leveraging the unidirectional multi‐effect compression technique, the topological network reorganization of foam is induced, transforming the initial circular open‐cell structure into a re‐entrant cell structure. This structural transformation endows the foam with stable NPR capability, achieving a minimum Poisson's ratio value of −0.4 within 30% compressive strain. Benefiting from its reinforced network structure, the foam also demonstrates high compressive strength (6.47 MPa) and tensile strength (1.67 MPa). Furthermore, it is recyclable and can be recompressed into thermosetting films. This work offers a straightforward approach to making auxetic thermosetting foams with good mechanical and recyclable properties, which is interesting for the development of high‐performance auxetic materials.

Unraveling the reinforcing mechanisms for cementitious composites with 3D printed multidirectional auxetic lattices using X-ray computed tomography

This study investigates the mechanical properties of cementitious composites with 3D-printed auxetic lattices, featuring negative Poisson’s ratios (auxetic behavior) in multiple directions. These lattices were fabricated using vat photopolymerization 3D printing, and three base materials with varying stiffness and deformation capacities were analyzed to determine their impact on the composites’ mechanical behavior. To unravel the reinforcing mechanisms of multidirectional auxetic lattices, which exhibit auxetic behavior in both planar and out-of-plane directions, X-ray computed tomography (X-ray CT) was utilized to analyze composite damage evolutions under different strain levels. The micro-CT characterization reveals that auxetic lattices more effectively constrain crack growth and dissipate energy by distributing stress evenly within the cement matrix. In contrast, due to lack of lateral confinement, the non-auxetic lattice reinforced composites primarily dissipate energy through extensive crack propagation and interfacial damage, leading to lower peak strength. When strain exceeding 5%, although the confinement from the auxetic behavior diminished with crack propagation, the lattice can still maintain the composite’s structural integrity, resulting in 1.7 times higher densification energy than conventional cement-based materials. These findings provide valuable insights for designing auxetic lattice-reinforced cementitious composites with enhanced load-bearing capacity and improved dissipation capabilities.

A biomimetic chiral auxetic vertebral meta-shell

Abstract The work presents a novel thin-walled biomimetic auxetic meta-shell for patient-specific vertebral orthopedic implants. The proposed design stemmed from the concept of an intrinsically multiple curved auxetic meta-structure, which is created by folding a 2D bio-inspired chiral geometry according to the morphology of human vertebral cortical bones. Through a multi-view stereo Digital Image Correlation (DIC) system, we investigated the mechanical response of a bio-grade titanium (Ti6Al4V ELI) additively manufactured prototype of the meta-structure under compressive loadings. In addition, we analyzed the morphology of the prototype using a scanning electron microscopy (SEM) and an optical image dimension measurement system both before and after compressive tests. An accurate Finite Element model, which exactly reproduced the geometry of the 3D printed meta-shell, was implemented and calibrated against experimental results, obtaining a precise prediction tool of its mechanical response. The findings of this work demonstrate that the designed meta-shell shows a peculiar auxetic behavior, a targeted stiffness matching to that of human vertebral bone tissues and a higher global elastic strain capability compared to those of monolithic traditional vertebral body replacements.


Exploring the dependencies of Poisson's ratio in auxetic structures

AbstractAuxetic materials are mostly known for their negative Poisson's ratio, a parameter used to describe the deformation behavior of structures. This ratio serves a similar role as a material constant, detailing behavior on a microscopic scale. However, the deformation behavior of complex auxetic structures cannot be described completely using the classical Poisson's ratio approach. While it may suffice to describe auxetic behavior in foams or crystals, it fails for larger scales like the auxetic lattice structures, discussed in this study. To address this limitation, an extension to the classical Poisson's ratio is proposed to better describe the behavior of such structures. The developed method shows the different dependencies, namely the directional dependency, the frequency dependency and the position dependency of auxetic unit cells.

Analysis of Mechanical Properties and Parameter Dependency of Novel, Doubly Re-Entrant Auxetic Honeycomb Structures.

This study proposes a new, doubly re-entrant auxetic unit-cell design that is based on the widely used auxetic honeycomb structure. Our objective was to develop a structure that preserves and enhances the advantages of the auxetic honeycomb while eliminating all negative aspects. The doubly re-entrant geometry design aims to enhance the mechanical properties, while eliminating the buckling deformation characteristic of the re-entrant deformation mechanism. The effects of the geometric modification are described and evaluated using two parameters, offset and deg. A series of experiments were conducted on a wide range of parameters based on these two parameters. Specimens were printed via the vat photopolymerization process and were subjected to a compression test. Our aim was to investigate the mechanical properties (energy absorption and compressive force) and the deformation behaviour of these specimens in relation to the relevant parameters. The novel geometry achieved the intended properties, outperforming the original auxetic honeycomb structure. Increasing the offset and deg parameters results in increasing the energy absorption capability (up to 767%) and the maximum compressive force (up to 17 times). The right parameter choice eliminates buckling and results in continuous auxetic behaviour. Finally, the parameter dependency of the deformation behaviour was predicted by analytical approximation as well.

A multi-step auxetic metamaterial with instability regulation

A stable deformation mode is highly desired for mechanical metamaterials, especially when coupled with a negative Poisson’s ratio. However, such metamaterials often face challenges in terms of scalability toward large deformation or strain. In response, we propose a multi-step hierarchical auxetic metamaterial design paradigm, incorporating a series of incrementally scaled-down structures with same scale factor α into a re-entrant framework. This design enables instability regulation and multi-step deformation capabilities while preserving auxetic behavior, even under significant strain. Such multi-step metamaterials exhibit excellent properties, including tailored multi-phase compression modulus and strength, along with an enhanced energy absorption capacity that is as large as 2.1 times that of the original auxetic metamaterial. Experiments and simulations demonstrate that the deformation mechanism and compression response of the proposed multi-step auxetics are strongly influenced by the reduction factor and the order of the inner structure. A particularly intriguing observation is that the incorporation of embedded microstructures can restore stable deformation, even in the presence of significant initial instability, particularly with a reduction factor of 1/5. At high relative density, its specific energy absorption stands out favorably compared to other configurations, highlighting the success of the recoverable buckling mechanism. This work paves the way for designing multi-step mechanical metamaterials for use in impact resistance and body protection.

Poisson function and volume ratio of soft anisotropic materials under large deformations

Accurate transverse deformation measurements are required for the estimation of the Poisson function and volume ratio. In this study, pure silicone and soft composite specimens were subjected to uniaxial tension, and the digital image correlation method was used to measure longitudinal and in- and out-of-plane transverse stretches. To minimize the effects of measurement errors on parameter estimation, the measured transverse stretches were defined in terms of the longitudinal stretch using a new formulation based on Poisson's ratios and two stretch-dependent parameters. From this formulation, Poisson functions and volume ratio for soft materials under large deformations were obtained. The results showed that pure silicone can be considered isotropic and nearly incompressible under large deformations, as expected. In contrast, Poisson's ratio of silicone reinforced with extensible fabric can exceed classical bounds, including negative value (auxetic behavior). The incompressibility assumption can be employed for describing the stress-stretch curve of pure silicone, while volume ratios are required for soft composites. Data of human skin, aortic wall, and annulus fibrosus from the literature were selected and analyzed. Except for the aortic wall, which can be considered nearly incompressible, the studied soft tissues must be regarded as compressible. All tissues presented anisotropic behavior.

A yarn-to-fabric multiscale modeling strategy for auxetic behavior analysis of negative Poisson’s yarn-based fabric

Auxetic behavior is critical to determining the deformation and mechanical performance of materials. Auxetic mechanisms of the woven fabric have previously not been well understood, especially for those containing negative Poisson’s ratio yarn (NPRY). Most theoretical models were developed from the macro geometric structure which lacks analysis of yarn levels. This paper aims to use numeral analysis combined with finite element modeling to investigate the auxetic behavior of the NPRY-based fabric. Firstly, the theoretical model that reveals the relationship between the auxetic behaviors of yarn and NPRY-based fabric was established based on component yarn interweaving rules, deformation, and stress. Following, a strain-dominated deformation simulation was further performed to clarify the micro stress and auxetic mechanism of fabric by calculating the stress–strain response and NPR value. Moreover, the experiments of NPRY-based fabric were also developed to validate the theoretical and simulation results, Results indicate that the model can well predict the auxetic behavior of fabric with an error under 7%. The micro–macro analysis of the auxetic behavior from yarn to fabric provides a fundamental understanding of the auxetic mechanism of NPRY-based fabric. Additionally, the yarn-to-fabric model can used to study the auxetic behavior of NPR fabric with variable parameters thus supplying theoretical guidance for engineering.

Interplay of chromatin organization and mechanics of the cell nucleus

The nucleus of eukaryotic cells is constantly subjected to different kinds of mechanical stimuli, which can impact the organization of chromatin and, subsequently, the expression of genetic information. Experiments from different groups showed that nuclear deformation can lead to transient or permanent condensation or decondensation of chromatin and the mechanical activation of genes, thus altering the transcription of proteins. Changes in chromatin organization, in turn, change the mechanical properties of the nucleus, possibly leading to an auxetic behavior. Here, we model the mechanics of the nucleus as a chemically active polymer gel in which the chromatin can exist in two states: a self-attractive state representing the heterochromatin and a repulsive state representing euchromatin. The model predicts reversible or irreversible changes in chromatin condensation levels upon external deformations of the nucleus. We find an auxetic response for a broad range of parameters under small and large deformations. These results agree with experimental observations and highlight the key role of chromatin organization in the mechanical response of the nucleus.

Periodic tetrahedral auxetic metamaterial

In this work, we introduce a novel three-dimensional auxetic mechanical metamaterial consisting of rotating tetrahedra connected by ideal hinges at their vertices, arranged to form a periodic framework structure. Through analytical and kinematic approaches, we evaluated the deformation behavior of the proposed idealized model, revealing Poisson’s ratios ranging between −0.36 and −2.72 and a transverse isotropic response as a result of its geometry. A specimen of the proposed metamaterial concept is designed by introducing deformable ribs between the solid units, and fabricated via additive manufacturing in polymeric material. Auxetic behavior of the prototype was assessed through a compression test and accurately predicted by a full-scale Finite Element model. We envisage that this new metamaterial design can have a significant impact on a wide range of engineering applications, particularly as bone substitute biomaterial.

Hierarchical design of auxetic metamaterial with peanut-shaped perforations for extreme deformation: Self-similar or not?

Hierarchical designs have exhibited great potential in reducing structural weight and improving mechanical properties. However, the hierarchical design of perforated auxetic metamaterials with curved holes is rarely investigated and the choice of self-similar hierarchical design or not still confuses us. In this study, two types of hierarchical designs with self-similar and non-self-similar features for the auxetic metamaterial with peanut-shaped perforations are realized and compared. First, the printed hierarchical auxetic metamaterials via additive manufacturing technology are tested by quasi-static tension to explore their mechanical performance in different directions. Correspondingly, the computational homogenization model is established to characterize their full elastic properties and its effectiveness is verified by the experimental results. Subsequently, the deformation mechanisms of the proposed hierarchical metamaterials are numerically analyzed to address the superiority of self-similar design over the non-self-similar design. Finally, the influences of microstructural parameters and hierarchy order on the effective elastic constants of the proposed hierarchical metamaterial are considered and the optimal topology with extreme auxetic behavior is recommended. The results indicate that the proposed self-similar hierarchical design exhibits significant anisotropic feature, which can serve the multidirectional mechanical requirements, and the remarkable enhancement in auxeticity can be attributed to the synergistic deformation of tetrachiral sub-elements. Besides, the increase of hierarchy order does not continuously enhance the auxetic behavior of hierarchical metamaterial, although it can effectively change the porosity of structure. Through such investigations, a meaningful guidance of property map is provided for the hierarchical design of auxetic metamaterial perforated by curved cuts.

Auxetic enhancement of the shunted piezoelectric effect for vibration suppression

Shunted piezoelectric patches connected to passive electric circuits can be attached to a host structure for effective vibration attenuation. The effect of an auxetic layer to enhance the electromechanical coupling and subsequently the vibration suppression is studied here. Three different configurations are considered for the layer: a classical, a homogeneous auxetic and a layer with microstructure leading to auxetic behavior. First, is presented a modification of the “current-flowing” shunt circuit for multimode vibration control. Two finite element models have been validated, the frequency response graph of the system and the most suitable values of the electric parameters are calculated and a comparison is provided. Furthermore, it is shown that the vibration reduction of the second and third eigenmodes can be enhanced, provided that an auxetic of significant thickness is used. The results demonstrate the effect of the auxetic boosting on vibration suppression.

Shape Morphing of Re‐Entrant Honeycomb Metamaterials for Linear Auxetic Behaviors

A re‐entrant honeycomb structure stands out as one of the most prevalent auxetic metamaterials, characterized by its negative Poisson's ratio. While re‐entrant auxetic structures are capable of achieving tunable Poisson's ratios, they tend to vary with the magnitude of applied strain, thereby exhibiting nonlinear auxetic behaviors. This study proposes a novel re‐entrant structure aimed at achieving linear auxetic behavior by mathematically modifying the shape of a re‐entrant cell. To achieve this objective, a sigmoid‐based shape morphing function is introduced to modify the morphology of the hinge connections within the re‐entrant honeycomb cell. The deformation behavior of the shape‐morphed re‐entrant cell is investigated using finite element analysis (FEA), with variations in the morphing parameter. Two FEA models, namely the unconstrained and constrained models, are developed for fundamental analysis of cell deformation and experimental validation, respectively. Compared to the pure re‐entrant honeycomb structure, the proposed shape morphing reduces the relative variation of Poisson's ratio by 70%, while maintaining its magnitude higher than 1.0. This achievement of linear auxetics with a high Poisson's ratio has the potential to broaden the applications of the proposed auxetic structures to various functional components, including sensors with high linear sensitivity and soft actuators with tunable deformation characteristics.

Structure-Property Relationships in Auxetic Liquid Crystal Elastomers-The Effect of Spacer Length.

Auxetics are materials displaying a negative Poisson's ratio, i.e., getting thicker in one or both transverse axes when subject to strain. In 2018, liquid crystal elastomers (LCEs) displaying auxetic behaviour, achieved via a biaxial reorientation, were first reported. Studies have since focused on determining the physics underpinning the auxetic response, with investigations into structure-property relationships within these systems so far overlooked. Herein, we report the first structure-property relationships in auxetic LCEs, examining the effect of changes to the length of the spacer chain. We demonstrate that for LCEs with between six and four carbons in the spacer, an auxetic response is observed, with the threshold strain required to achieve this response varying from 56% (six carbon spacers) to 81% (four carbon spacers). We also demonstrate that Poisson's ratios as low as -1.3 can be achieved. Further, we report that the LCEs display smectic phases with spacers of seven or more carbons; the resulting internal constraints cause low strains at failure, preventing an auxetic response. We also investigate the dependence of the auxetic threshold on the dynamics of the samples, finding that when accounting for the glass transition temperature of the LCEs, the auxetic thresholds converge around 56%, regardless of spacer length.