Non-chiral, molecular model of negative Poisson ratio in two dimensions

Auxeticity Tuning by Nanolayer Inclusion Ordering in Hard Sphere Crystals

Designing a particular change in a system structure to achieve the desired elastic properties of materials for a given task is challenging. Recent studies of purely geometrical atomic models have shown that structural modifications on a molecular level can lead to interesting and desirable elastic properties. Still, the result of such changes is usually difficult to predict. The present work concerns the impact of nanolayer inclusion ordering in hard sphere crystals on their elastic properties, with special attention devoted to their auxetic properties. Two sets of representative models, based on cubic crystals consisting of 6×6×6 unit cells of hard spheres and containing either neighboring or separated layers of spheres of another diameter, oriented orthogonally to the [001] direction, have been studied by Monte Carlo simulations in the isothermal-isobaric (NpT) ensemble. Their elastic constants have been evaluated using the Parinello-Rahman approach. The Monte Carlo simulations showed that introducing the layer inclusions into a pure face-centered cubic (FCC) structure leads to the system's symmetry changes from cubic symmetry to tetragonal in both cases. Essential changes in the elastic properties of the systems due to layer ordering were found both for neighboring and separated inclusions. It has been found that the choice of a set of layer inclusions allows one to tune the auxetic properties in two crystallographic directions ([110][11¯0] and [101][1¯01]). In particular, this study revealed that the change in layer ordering (from six separated layers to six neighboring ones) allows for, respectively: (i) enhancing auxeticity of the system in the [101][1¯01] direction with almost loss of auxetic properties in the [110][11¯0] direction in the case of six separated layers, while (ii) in the case of six neighboring layers, keeping the auxetic properties in both auxetic directions independently of the size of spheres constituting inclusions.

Investigation and Tailoring of Rotating Squares' and Rectangles' Auxetic Structure Behavior through Computational Simulations of 6082T6 Aluminum Alloy Structures

Auxetic structures, renowned for their unique lateral expansion under longitudinal strain, have attracted significant research interest due to their extraordinary mechanical characteristics, such as enhanced toughness and shear resistance. This study provides a systematic exploration of these structures, constructed from rigid rotating square or rectangular unit cells. Incremental alterations were applied to key geometrical parameters, including the angle (θ) between connected units, the side length (a), the side width (b) of the rotating rigid unit, and the overlap distance (t). This resulted in a broad tunable range of negative Poisson's ratio values from -0.43 to -1.78. Through comprehensive three-dimensional finite-element analyses, the intricate relationships between the geometric variables and the resulting bulk Poisson's ratio of the modeled auxetic structure were elucidated. This analysis affirmed the auxetic behavior of all investigated samples, characterized by lateral expansion under tensile force. The study also revealed potential stress concentration points at interconnections between rotating units, which could impact the material's performance under high load conditions. A detailed investigation of various geometrical parameters yielded fifty unique samples, enabling in-depth observation of the impacts of geometric modifications on the overall behavior of the structures. Notably, an increase in the side width significantly enhanced the Poisson's ratio, while an increase in the overlap distance notably reduced it. The greatest observable change in the Poisson's ratio was a remarkable 202.8%, emphasizing the profound influence of geometric parameter manipulation. A cascaded forward propagation-backpropagation neural network model was deployed to determine the Poisson's ratio for auxetic structures, based on the geometric parameters and material properties of the structure. The model's architecture consisted of five layers with varying numbers of neurons. The model's validity was affirmed by comparing its predictions with FEA simulations, with the maximum error observed in the predicted Poisson's ratio being 8.62%.

Auxeticity of monolayer, few-layer, vdW heterostructure and ribbon penta-graphene

Using molecular statics simulations, we specifically focus on investigating the negative Poisson's ratio of the monolayer, few-layer, van der Waals, and ribbon penta-graphene. As a result, we provide evidence to show that the Poisson's ratio is the combination of bond stretching and angle rotating mechanism. The auxeticity of monolayer penta-graphene is due to the dominance of bond stretching. However, the significant effect of the angle rotating mechanism causes the enhancement of the in-plane Poisson's ratio of few-layer penta-graphene. Furthermore, the elongation of interlayer bonds results in a negative out-of-plane Poisson's ratio in few-layer penta-graphene. The strong dependence of Poisson's ratio on stacking configuration and number of layers was found. We also show that the van der Waals interaction slightly enhances the auxeticity of heterostructure penta-graphene. Finally, we discuss the significant effects of warped edges on the auxeticity of penta-graphene ribbons.

Direct Writing of Functional Layer by Selective Laser Sintering of Nanoparticles for Emerging Applications: A Review

Selective laser sintering of nanoparticles enables the direct and rapid formation of a functional layer even on heat-sensitive flexible and stretchable substrates, and is rising as a pioneering fabrication technology for future-oriented applications. To date, laser sintering has been successfully applied to various target nanomaterials including a wide range of metal and metal-oxide nanoparticles, and extensive investigation of relevant experimental schemes have not only reduced the minimum feature size but also have further expanded the scalability of the process. In the beginning, the selective laser sintering process was regarded as an alternative method to conventional manufacturing processes, but recent studies have shown that the unique characteristics of the laser-sintered layer may improve device performance or even enable novel functionalities which were not achievable using conventional fabrication techniques. In this regard, we summarize the current developmental status of the selective laser sintering technique for nanoparticles, affording special attention to recent emerging applications that adopt the laser sintering scheme.

Negative out-of-plane Poisson's ratio of bilayer graphane

With its excellent mechanical and thermal properties, bilayer graphane is a promising material for realizing future nanoelectromechanical systems. In this study, we focus on the auxetic behavior of bilayer graphane under external loading along various directions through atomistic simulations. We numerically and theoretically reveal the mechanism of the auxeticity in terms of intrinsic interactions between carbon atoms by constructing bilayer graphane. Given that the origin of the auxeticity is intrinsic rather than extrinsic, the work provides a novel technique to control the dimensions of nanoscale bilayer graphane by simply changing the external conditions without the requirement of complex structural design of the material.

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.

Using Finite Element Approach for Crashworthiness Assessment of a Polymeric Auxetic Structure Subjected to the Axial Loading

Polyurethane foams are one of the most common auxetic structures regarding energy absorption enhancement. This present study evaluates the result reliability of two different numerical approaches, the H-method and the P-method, to obtain the best convergence solution. A polymeric re-entrant cell is created with a beam element and the results of the two different methods are compared. Additionally, the numerical results compare well with the analytical solution. The results show that there is a good agreement between converged FE models and the analytical solution. Regarding the computational cost, the P-method is more efficient for simulating the re-entrant structure subjected to axial loading. During the second part of this study, the re-entrant cell is used for generating a polymeric auxetic cellular tube. The mesh convergence study is performed on the cellular structures using the H- and P- methods. The cellular tube is subjected to tensional and compressive loading, the module of elasticity and Poisson’s ration to calculate different aspect ratios. A nonlinear analysis is performed to compare the dynamic response of a cellular tube versus a solid tube. The crashworthiness indicators are addressed and the results are compared with equivalent solid tubes. The results show that the auxetic cellular tubes have better responses against compressive loading. The primary outcome of this research is to assess a reliable FE approach for re-entrant structures under axial loading.

Poisson's Ratio of the f.c.c. Hard Sphere Crystals with Periodically Stacked (001)-Nanolayers of Hard Spheres of Another Diameter

The results of studies on the influence of periodically stacked nanolayer inclusions, introduced into the face-centered cubic (f.c.c.) hard sphere crystal, on Poisson's ratio of the obtained nanocomposite system are presented. The monolayers are orthogonal to the [ 001 ] -direction. They are formed by hard spheres with diameter different from the spheres forming the matrix of the system. The Monte Carlo computer simulations show that in such a case the symmetry of the system changes from the cubic to tetragonal one. When the diameter of the inclusion spheres increases at certain range, a decrease of the negative Poisson's ratio in the [ 101 ] [ 1 ¯ 01 ] -directions is observed, i.e., the system enhances its partial auxeticity. The dependence of the maximal, average, and negative parts of the minimal Poisson's ratio on the direction of the applied load are shown in a form of surfaces in spherical coordinates, plotted for selected values of nanolayer particle diameters. The most negative value of the Poisson's ratio found among all studied systems was - 0.11 (at pressure p * = 100 , which is about ten times higher than the melting pressure) what is almost twice more negative than in the f.c.c. crystal of identical hard spheres. The observed effect weakens along with the decrease of pressure and becomes hardly noticeable near melting. This study indicates that modifying only the size of the inclusion particles one can change Poisson's ratio of nanocomposites at high pressures.

Filtration Properties of Auxetics with Rotating Rigid Units

Auxetic structures and materials expand laterally when stretched. It has been argued that this property could be applied in the design of smart filters with tunable sieving properties. This work analyses the filtration properties of a class of auxetic structures which achieve their auxeticity through a rotating rigid unit mechanism, an archetypal mechanism known to be responsible for this behavior in a number of crystalline materials. In particular, mathematical expressions are derived for the space coverage of networks constructed from a variety of quadrilaterals, as well as the pore radius. The latter is indicative of the particle size that can pass through when the particle dimension is comparable to the pore size, whereas the space coverage is indicative of the rate of flow when the particles are of a much smaller dimension than the pore size. The expressions suggest that these systems offer a wide range of pore sizes and space coverages, both of which can be controlled through the way that the units are connected to each other, their shape and the angle between them.

Finite Element Analysis of Tunable Composite Tubes Reinforced with Auxetic Structures

A tubular composite structure that is built of two materials, characterized by different Young moduli, is analysed in this paper. The Young's modulus of one of these materials can be controlled by external conditions e.g., magnetic or electric field, temperature etc. The geometry of the reinforcement is based on typical auxetic re-entrant honeycomb cellular structure. The influence of this external factor on the behaviour of the stretched tube is analysed in this paper. Also, the possibility of creating a tubular composite structure whose cross-section is either shrinking or expanding, while stretching the tube is presented.

Auxeticity of Yukawa Systems with Nanolayers in the (111) Crystallographic Plane

Elastic properties of model crystalline systems, in which the particles interact via the hard potential (infinite when any particles overlap and zero otherwise) and the hard-core repulsive Yukawa interaction, were determined by Monte Carlo simulations. The influence of structural modifications, in the form of periodic nanolayers being perpendicular to the crystallographic axis [111], on auxetic properties of the crystal was investigated. It has been shown that the hard sphere nanolayers introduced into Yukawa crystals allow one to control the elastic properties of the system. It has been also found that the introduction of the Yukawa monolayers to the hard sphere crystal induces auxeticity in the [ 11 1 ¯ ] [ 112 ] -direction, while maintaining the negative Poisson's ratio in the [ 110 ] [ 1 1 ¯ 0 ] -direction, thus expanding the partial auxeticity of the system to an additional important crystallographic direction.

Metal [100] Nanowires with Negative Poisson's Ratio

When materials are under stretching, occurrence of lateral contraction of materials is commonly observed. This is because Poisson's ratio, the quantity describes the relationship between a lateral strain and applied strain, is positive for nearly all materials. There are some reported structures and materials having negative Poisson's ratio. However, most of them are at macroscale, and reentrant structures and rigid rotating units are the main mechanisms for their negative Poisson's ratio behavior. Here, with numerical and theoretical evidence, we show that metal [100] nanowires with asymmetric cross-sections such as rectangle or ellipse can exhibit negative Poisson's ratio behavior. Furthermore, the negative Poisson's ratio behavior can be further improved by introducing a hole inside the asymmetric nanowires. We show that the surface effect inducing the asymmetric stresses inside the nanowires is a main origin of the superior property.

A near-zero Poisson's ratio of Si with ordered nanopores

Significant reduction in the Poisson's ratio is predicted for Si with cylindrical nanopores through first-principles DFT calculations.

On the auxetic properties of generic rotating rigid triangles

Materials having a negative Poisson's ratio (auxetic) get fatter rather than thinner when uniaxially stretched. This phenomenon has been often explained through models that describe how particular geometric features in the micro or nanostructure of the material deform when subjected to uniaxial loads. Here, a new model based on scalene rigid triangles rotate relative to each other will be presented and analysed. It is shown that this model can afford a very wide range of Poisson's ratio values, the sign and magnitude of which depends on the shape of the triangles and the angles between them. This new model has the advantage that it is very generic and may be potentially used to describe the properties in various types of materials, including auxetic foams and their relative surface density. Specific applications of this model, such as a blueprint for a system that can exhibit temperature-dependent Poisson's ratios, are also discussed.

Locally auxetic behavior of elastomeric polypropylene on the 100 nm length scale

We observe unexpected locally auxetic behavior in elastomeric polypropylene, a semicrystalline polymer with a natural microstructure and a low degree of crystallinity. Our series of scanning force microscopy images show the nanomechanical deformation processes that occur upon stretching a thin film of elastomeric polypropylene. Upon uniaxial stretching, the angle between epitaxially grown lamella branches remains constant and the lamellae elongate, resulting in locally auxetic behavior (negative Poisson's ratio) on the 100-nanometer scale. This mechanism causing auxetic behavior, which was previously proposed on the basis of geometric arguments, appears to be an intrinsic property of certain semicrystalline polymers.

Auxetic Cellular Materials and Structures

Auxetic materials and structures exhibit the very unusual property of becoming wider when stretched and narrower when squashed (i.e. they have a negative ‘Poisson’s ratio’). This property results in many beneficial effects in the characteristics of the system that make auxetics superior to conventional systems in many practical and high tech applications, including aeronautics where, for example, auxetics are being proposed as potential components for the production of better quality lifting devices such as helicopter rotor blades or airplane wings. This work reviews and discusses the behaviour of known and novel cellular systems, which exhibit this unusual but highly desirable property.