Auxetic Materials Research Articles

Germanether: a two-dimensional auxetic semiconductor with tunable direct-band-gap and high electron mobility

Pristine germanene is a zero-gap semi-metal, which may hinder its practical application in semiconducting devices. Here, on the basis of the structural characteristics of digermyl ether, we theoretically design a two-dimensional crystal, namely germanether. Germanether exhibits excellent dynamical and thermal stability. It possesses an indirect band gap of 1.37 eV and a high electron mobility of 2.32 × 103 cm2 V−1 s−1. The uniaxial strain and layer stacking order can trigger an indirect-to-direct band gap transition. More interestingly, germanether has remarkable in-plane negative Poisson’s ratios with the largest one (∼−0.2) five times of borophenes and three times of penta-graphene. The negative Poisson’s ratio arises from the interplay of Ge–O tetrahedron symmetry and Ge-4d orbitals involvement, which is different from previously reported auxetic materials. All these findings render germanether is a competitive material for the future application in nanomechanics and nanoelectronics.

Correction to: Bending-Dominated Auxetic Materials for Wearable Protective Devices Against Impact

A correction to this paper has been published: https://doi.org/10.1007/s40870-021-00311-w

Tunable compressive properties of a novel auxetic tubular material with low stress level

The auxetic tubular materials have attracted wide attention owing to their unusual mechanical properties and potential applications in designing foldable devices. However, most of auxetic tubular structures designed by incorporating re-entrant, chiral or penetrated microstructures remain great challenging in stress concentration because of the presence of shape corners in these structures. In this study, a novel auxetic tubular structure is designed by incorporating the smooth peanut-shaped hole pattern and then is fabricated via 3D printing technique. Subsequently its mechanical properties and deformation characteristics are investigated by uniaxial compression experiments and finite element simulation. Results reveal that the designed tube exhibits significant auxetic performance under compression and the stress level within the structure is significantly reduced, in contrast to the auxetic tubular structure with orthogonal elliptical hole pattern. Finally, the effect of controlling parameters of the designed auxetic tubular structure on Poisson’s ratio is studied to better understand its auxetic behavior and also provide tunable design of auxetic tubular structures.

Mechanotropism of single cells adhering to elastic substrates subject to exogenous forces

Adherent cells are able to actively generate internal forces, channelled by cytoskeletal protein filaments and transmitted through transmembrane receptors to the surrounding environment by means of focal adhesions. Cells also dynamically interact with extracellular matrix by sensing external chemo-mechanical stimuli and then inducing formation of stress fibres mediated by polymerization/de-polymerization processes which continuously redesign the interplay between structural organization and contractility activities in the cytoskeleton, so orchestrating selected signal pathways at the basis of many important cell’s physiological functions like adhesion, migration and division. Despite chemo- and duro-taxis have been intensively studied in the last years to understand how cells move on a substrate, their polarization and reorientation – observed during gastrulation, wound healing and morphogenesis – are only partially understood. By starting from the evidence highlighted in some recent studies that cells reorient in response to substrata deformation by essentially obeying a pure mechanical interaction, we propose to interpret the seeming overall cells’ rotation resulting from the reconfiguration of their cytoskeleton – here named mechanotropism – as a nonlinear optimization problem in which the adherent cell aims to align along directions leading it to minimize a physically coherent measure of work spent to deform the elastic substrate while retaining a prescribed level of homeostatic contractile force. To do this, the single-cell is simply modelled as a finite size contractile force dipole that acts on the boundary of a half-space perturbed by applied point loads. The effects of fences of forces acting orthogonally and tangentially on the boundary of the adhesion medium and encircling the cell are then investigated, so obtaining solutions that predict multiple non-trivial cell polarizations as functions of number, direction, relative magnitude and distance from the cell-dipole of the forces, as well as of the substrate’s Poisson ratio, with unprecedented outcomes under the hypothesis of auxetic (i.e. negative Poisson ratio) materials. The results lead to envisage that the proposed theoretical model might contribute to unveil the mechanobiological principles ruling in vivo cells orientation processes by guiding the design of novel experimental strategies and to conceive new mechanics-based markers for guessing cells’ pathological conditions from their mechanotropism.

Novel hybrid auxetic structures for improved in- plane mechanical properties via additive manufacturing

Auxetic metamaterials have evolved growing beyond the cellular material structures and offering unique combinations of both auxetic and mechanical properties. However, the understanding and development of these promising material structures have been predominantly based on analytical evaluation methods, as practical implementation was restricted by manufacturing limitations. The manufacturing limitation has changed quite significantly with the advent of additive manufacturing methods, particularly with direct metal printing, such as selective laser melting. Ever since, the auxetic meta material structures began attracting renewed interests, and several different new structural forms and hybridisation of certain existing models followed, focussing specifically on enhancing auxeticity as well as other mechanical attributes. A recently developed and novel S-shaped unit cell based auxetic structure is hybridised with star re-entrant unit cells and analysed both numerically and experimentally based on physical forms produced by selective laser melting as part of the research reported here. Numerical and experimental results correlated sufficiently, depitcing significant enhanced auxeticity as high as −3, and mechanical property with the hybrid structures.

Analysis of auxetic core sandwich beams subjected to transversely localized loads using two-dimensional symplectic elasticity approach

It is well known that sandwich structures containing low-density soft cores are susceptible to transversely localized loads. However, multi-parameter foundation models of the sandwich cores are extremely simplified when the structures are composed of auxetic materials, whose Poisson’s ratios play very important roles in the face–core interaction. In this study, a two-dimensional symplectic elasticity model of a beam–foundation system representing sandwich beams subjected to normal surface tractions is formulated. The effects of the foundation properties, including Poisson’s ratio ranging from positive to negative, are presented. The proposed technique is beneficial for the potential usage of auxetic core materials.

Enhanced fatigue performance of auxetic honeycomb/substrate structures under thermal cycling

This paper studies the fatigue behavior of auxetic honeycomb layer/substrate structures due to interfacial delamination damage. First, the interfacial thermal stress and cyclic interfacial thermal stress intensity factor (ITSIF) at the free ends of the structure are determined in terms of the thermal shock time, relative density, aspect ratio, and internal cell angle of the honeycomb. Then, a theoretical model for the service life analysis of the structures is established based on Paris's law. The results show that the auxetic structures have a lower ITSIF level and a longer service life compared with those of the non-auxetic structures. Another interesting finding is that a reduction in the relative density of the honeycomb layer will increase the service life of the structures. This confirms the significance of applying auxetic materials in re-usable structures for thermal protection purposes. This research is the first attempt to evaluate the service life of the auxetic honeycomb layer/substrate structures under thermal cycling.

On the Problematic Case of Product Approximation in Backus Average

Elastic anisotropy might be a combined effect of the intrinsic anisotropy and the anisotropy induced by thin-layering. The Backus average, a useful mathematical tool, allows us to describe such an effect quantitatively. The results are meaningful only if the underlying physical assumptions are obeyed, such as static equilibrium of the material. We focus on the only mathematical assumption of the Backus average, namely, product approximation. It states that the average of the product of a varying function with a nearly constant function is approximately equal to the product of the averages of those functions. We analyse particular problematic case for which the aforementioned assumption is inaccurate. Furthermore, we focus on the seismological context. We examine the inaccuracy’s effect on the wave propagation in a homogenous medium—obtained using the Backus average—equivalent to thin layers. Numerical simulations indicate clearly that the product approximation inaccuracy has negligible effect on wave propagation; irrespective of layers’ symmetries. To give the results a practical focus, we show that the problematic case of product approximation is strictly related to the negative Poisson’s ratio of constituents layers. We discuss the laboratory and well-log cases in which such a ratio has been noticed. Upon thorough literature review, it occurs that examples of so-called auxetic materials (media that have negative Poisson’s ratio) are not extremely rare exceptions as thought previously. The investigation and derivation of Poisson’s ratio for materials exhibiting symmetry classes up to monoclinic become a significant part of this paper. In addition to the main objectives, we also show that the averaging of cubic layers results in an equivalent medium with tetragonal (not cubic) symmetry. We present concise formulations of stability conditions for low symmetry classes, such as trigonal, orthotropic, and monoclinic.

A novel planar auxetic phononic crystal with periodic cookie-shaped cellular microstructures

The star-shaped auxetic structures with sharp reentrant corners are highly stressed in practice. In this article, a novel planar auxetic material is designed by introducing periodic cookie-shaped pattern to decrease the risk of structure failure. Then both auxetic and band gap properties are comprehensively investigated numerically. The results reveal that the stress level significantly decreases by an order of magnitude. Moreover, the designed structure can yield a large complete band gap in a much lower frequency region and has a good self-collimation effect. Finally, the parameter analysis allows one to tailor an auxetic phononic metamaterial with optimal acoustic and mechanical properties.

Electromechanical properties of ultra‐low porous auxetic piezocomposite: from the perspective of Poisson’s ratio

AbstractIn this study, the ultra‐low porous auxetic piezoelectric composite made of lead zirconate titanate (PZT) and hollow polyvinylidine difluoride (PVDF) is first proposed by combining “additive” and “subtractive” approaches. The electromechanical properties of the auxetic piezoelectric composite are investigated by finite element analysis. It is found that the ultra‐low porosity in the composite may lead to great extensibility along with the excellent figures of merit obtained in conventional highly porous piezoelectric ceramics. The small amount of additional PVDF can greatly tune the electromechanical properties of composite and effectively reduce the maximum stress of PZT. To elucidate the role of Poisson’s ratio on the electromechanical properties of piezoelectric materials, the relationship expressions among some electromechanical coefficients are derived. Moreover, the semi‐empirical expression of “longitudinal” compliance coefficients and a simple strategy for predicting some electromechanical coefficients are presented to instruct design and application of the ultra‐low porous auxetic piezoelectric materials.

Hybrid Auxetic Structures: Structural Optimization and Mechanical Characterization

With their increased energy absorption capacity, auxetic materials are perfectly fit to develop new, enhanced lightweight crash absorbers for cars. Herein, the mass distribution along the struts is optimized via finite element analysis with a parameterized optimization. Four different auxetic unit cells are taken from the literature and their struts parameterize, the models simulate, and the mass specific energy absorption capacity optimizes. The two models with the highest energy absorption capacity are then selected for experimental investigation and produced by additive manufacturing from a polymer. To further enhance the mechanical properties, the specimens are electrochemically coated with nickel and the polymer molten out by pyrolysis. Those Ni/polymer hybrids are subjected to quasistatic and dynamic impact experiments. Only a small strain rate sensitivity can be detected under dynamic loading, namely, a higher plastic collapse and higher plateau stress. The hollow struts are folding instead of bending, which render them much weaker than predicted by the simulation. In conclusion, it is possible to improve existing crash absorber elements with tailored auxetic hybrid structures. They absorb higher amounts of energy without changing their stiffness under dynamic loading while saving mass and cost.

Unique Omnidirectional Negative Poisson’s Ratio in δ-Phase Carbon Monochalcogenides

Auxetic materials (negative Poisson’s ratio) are of exceptional importance for nanomechanical applications. Using first-principles calculations, we propose two-dimensional δ-phase carbon monochalco...

Brief review of metamaterials and auxetic materials

This paper aims to provide a comprehensive review on auxetic materials and structures, including various types of cellular auxetics, natural and artificial auxetics, metallic auxetics, multi-material and composite auxetics. A material engineered to have aproperty that is not found in naturally occurring materials is the metamaterial (meaning"beyond" from the Greek word μετά meta, and "material" from the Latin word materia) made from assemblies of multiple elements shaped from composite materials such as metals and plastics. They have exceptional properties, derive from their geometrical shape rather than directly from the behavior of the base materials, in terms of mechanical response, energy absorption and, heat transport performance.One of the most studied species of mechanical metamaterials is the auxetic materials, a type of mechanical metamaterial with a negative Poisson’s ratio (which shrink transversely under longitudinal compression and expand transversely under longitudinal tension). They consistof numerous hinge-like cells that are joined together. The cells have a re-entrant geometry, i.e. under pressure, they expand in lateral direction.Superior and unusual properties of auxetics are presented and some existing or potential applications are summarized. Accompanied by uncommon deformation pattern under compression and tension, auxetic materials and structures are endowed with many desirable material properties, such as superior shear resistance, indentation resistance, fracture resistance, synclastic behavior, variable permeability and better energy absorption performance.

Numerical study of a re-entrant diamond structure under dynamic compression

Auxetic materials, due to its negative Poisson’s ratio, shrink laterally when compressed axially and expand laterally when pulled axially. A re-entrant diamond structure was developed by replacing the vertical walls in a conventional re-entrant structure with diamond cells, which featured cross-linking members to make them rigid. The incorporation of the rigid diamond unit cells increased the stiffness, strength, and energy absorption of the structure. A validated finite element (FE) model was adopted from previous work, and the structures were compressed at a speed of 5 m/s in the FE model. The independent geometrical parameters of the re-entrant diamond unit cell were re-entrant wall length (L1 ), diamond angle (θ2 ), and diamond wall length (L2 ). The FE model based on these values was thus used to investigate the influence of geometrical parameters (θ2 & L2/L1 ) on the deformation mode, stiffness, strength, and specific energy absorption (SEA) of the structure. The value of diamond angle (θ2 ) varied from 40° to 90° at intervals of 10°, while the length ratio (L2/L1 ) varied from 0.7 to 1.2 in increments of 0.1. The specific strength was used in the discussion to account for differences in the relative density of re-entrant diamond structures.

Mass production of re-entrant cubic auxetic structure

The unique characteristics of auxetic materials has attracted significant attention in the research domain. Its distinguishing negative Poisson’s ratio has found its way to targeted applications where normal materials fail to deliver the expected results. The manufacturing of macro sized auxetic structures has always been a challenge. This paper proposes the possibility for mass production of auxetic structures. Materials available in standard shapes are utilized to manufacture the auxetic structure. A new re-entrant cubic auxetic structure is developed, analysed and fabricated. This auxetic structure provides a better scope for mass production.

Two-dimensional ScN with high carrier mobility and unexpected mechanical properties

Two-dimensional (2D) semiconductors with desirable bandgaps and high carrier mobility have great potential in electronic and optoelectronic applications. In the present work, 2D M-ScN, H-ScN, and O-ScN are predicted by the swarm-intelligent global structure search method. The low formation energies and high dynamical and thermal stabilities indicate the high feasibility of experimental synthesis of these ScN monolayers. The electronic structure calculations reveal that M-ScN and O-ScN are both direct bandgap semiconductors with the bandgaps of 1.39 and 2.14 eV, respectively, while H-ScN has a large indirect bandgap of 3.21 eV. In addition, both M-ScN and H-ScN exhibit ultra-high electron mobilities (3.09 × 104 cm2 V−1 s−1 and 1.22 × 104 cm2 V−1 s−1, respectively). More notably, O-ScN is found to be a promising 2D auxetic and ferroelastic material. The values of negative Possion’s ratios and reversible strain of this monolayer are predicted to be −0.27% and 15%, respectively.

Assessment of the effect of negative Poisson’s ratio on the thermal postbuckling of temperature dependent FG-GRMMC laminated cylindrical shells

Auxetic materials have recently emerged as new types of advanced materials with unique material properties that conventional materials do not possess. In this paper, we examine the effect of in-plane negative Poisson’s ratio (NPR) on the thermal postbuckling behavior of graphene-reinforced metal matrix composite (GRMMC) laminated cylindrical shells. The shell consists of GRMMC layers arranged in a piece-wise functionally graded (FG) pattern and is subjected to a uniform thermal load surrounded by an elastic medium. Based on the molecular dynamics simulation results, it is noted that the temperature-dependent material properties of GRMMCs can be expressed as a nonlinear function of temperature. The thermal postbuckling problem of shells is modeled under the framework of the Reddy’s third order shear deformation theory and solved by using a singular perturbation technique in conjunction with a two-step perturbation approach. Numerical investigations are carried out for the postbuckling of (10/-10/10/-10/10)S and (10/-10/10)S shells with in-plane NPR. It is found that the FG-X pattern can enhance the buckling temperature and the thermal postbuckling strength of the shells. The anomaly is that the thermal buckling load and postbuckling strength of UD (10/-10/10)S shell are slightly higher than those of UD (10/-10/10/-10/10)S GRMMC laminated cylindrical shell.

Single-Layer BI: A Multifunctional Semiconductor with Ferroelectricity, Ultrahigh Carrier Mobility, and Negative Poisson’s Ratio

Developing two-dimensional multifunctional materials is highly desirable for nanoscale device applications. Herein, by means of first-principles calculations, we demonstrate a promising two-dimensional multifunctional semiconductor with ferroelectricity, ultrahigh carrier mobility, and negative Poisson's ratio in single-layer $\mathrm{BI}$. We show that single-layer $\mathrm{BI}$ exhibits intrinsic ferroelectricity, derived from its asymmetric structure, and the ferroelectricity features an in-plane electric polarization as large as $3.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}{\mathrm{C}}_{{\mathrm{m}}^{\ensuremath{-}1}}$, which is beneficial for nonvolatile memories. Owing to its large band dispersion, single-layer $\mathrm{BI}$ is also found to harbor an extremely high carrier mobility ($1.17\ifmmode\times\else\texttimes\fi{}{10}^{5}\phantom{\rule{0.1em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}{\mathrm{V}}^{\ensuremath{-}1}{\mathrm{s}}^{\ensuremath{-}1}$), even comparable to that of graphene, suggesting its potential for high-performance electronics and bulk photovoltaic effect. This, combined with the moderate band gap, renders single-layer $\mathrm{BI}$ with a high absorption coefficient (${10}^{5}\mathrm{cm}{\mathrm{m}}_{\ensuremath{-}1}$) from near-infrared to ultraviolet light. In addition, we unveil that single-layer $\mathrm{BI}$ is a long-sought-after auxetic material with a negative Poisson's ratio of \ensuremath{-}0.31. All of these findings make single-layer $\mathrm{BI}$ a compelling multifunctional material, offering a versatile platform for diverse nanoscale devices applications.

Tunable Positive/Negative Young's Modulus in Graphene‐Based Metamaterials

AbstractMechanical metamaterials exhibit unusual mechanical properties that originate from their topological design. Origami graphene may provide a platform for constructing novel carbon nanostructures. In the current study, a novel composite material that incorporates aligned graphene with localized origami shapes into the copper matrix is designed. Unlike many auxetic materials that have void phase, the proposed layer‐by‐layer assembled composite material appears to be solid in the microscopic scale. Based on the molecular dynamics (MD) simulations, it is observed that depending on the origami shapes, the in‐plane Poisson's ratio of origami graphene reinforced copper (100) composites can be tuned from positive to negative and, more importantly, it is discovered that the Young's modulus of the graphene/Cu composites can also be tuned from positive to negative in certain in‐plane directions.

Giant negative Poisson's ratio in two-dimensional V-shaped materials.

Two-dimensional (2D) auxetic materials with exceptional negative Poisson's ratios (NPR) are drawing increasing interest due to their potential use in medicine, fasteners, tougher composites and many other applications. Improving the auxetic performance of 2D materials is currently crucial. Here, using first-principles calculations, we demonstrated giant in-plane NPRs in MX monolayers (M = Al, Ga, In, Zn, Cd; X = P, As, Sb, S, Se, Te) with a unique V-shaped configuration. Our calculations showed that GaP, GaAs, GaSb, ZnS and ZnTe monolayers exhibit exceptional all-angle in-plane NPRs. Remarkably, the AlP monolayer possesses a giant NPR of −1.779, by far the largest NPR in 2D materials. The NPRs of these MX monolayers are correlated to the highly anisotropic features of the V-shaped geometry. The exotic mechanical properties of the V-shaped MX monolayers provide a new family of 2D auxetic materials, as well as a useful guidance for tuning the NPR of 2D materials.