Copper-Coordination Engineered Glassy Hydrogels Featuring Ultrastiffness and Structural Programmability.

In isotropic materials, it is known that values of Poisson's ratio larger than one half are thermodynamically inadmissible, for such values would lead to negative strain energy under certain loads. Although a negative Poisson's ratio is not forbidden by thermodynamics, it is rare in crystalline solids. With the development of modem fiber reinforced composite materials, the effective Poisson's ratio of laminated fiber reinforced composites shows a peculiar behavior as it becomes larger than one half or less than zero. In this article, a study of negative in-plane Poisson's ratio for a general class of randomly-oriented composite laminates is presented. A simple random statistical analysis has been presented. It is demonstrated that composite laminates with negative in-plane Poisson's ratio could be achieved by using the specific values of independent elastic constants E1, E2, G12, and v12 in each lamina. Also, the influence of the lamina material properties to the negative in-plane Poisson's ratio of the composite laminates is presented. The results from this statistical analysis provide a set of general guidelines for designing composite laminates with a special character-the negative in-plane Poisson's ratio.

Materials normally get thinner when stretched (positive Poisson’s ratio) and expand when heated (positive thermal expansion coefficients). However, not all systems behave in this way and systems (materials or structures) which defy common expectation and become wider when stretched (negative Poisson’s ratios, NPR, commonly referred to as auxetic) or contract when heated (negative thermal expansion, NTE) do exist and are now well documented. Materials exhibiting one of these unusual properties are known to be very useful in various practical applications. For example it has been shown that the presence of a negative Poisson’s ratio gives auxetic materials various enhanced physical characteristics over their conventional counterparts ranging from increased indentation resistance and a natural ability to form dome-shaped surfaces to improved acoustic damping properties. Similarly, negative thermal expansion materials can be extremely useful in various applications, such as in the manufacture of composites exhibiting some pre-determined thermal expansion coefficients since the presence of a component with negative thermal expansion lowers the overall thermal expansion of a composite. Although in recent years considerable progress and developments were made in the distinct fields of NPR and NTE, so far, research on systems which could exhibit both of these anomalous properties simultaneously is still in its infancy. Nevertheless, it is known that NTE and NPR are not mutually exclusive properties and in fact, single-crystalline polyacetylene networks (hypothetical carbon allotropes, which so far have not been synthesised) have been predicted to exhibit both properties. Here we will show how existing knowledge on systems exhibiting negative Poisson’s ratios and negative thermal expansion can be combined to produce a novel and easily constructible system which can exhibit both negative properties simultaneously. In particular, we note that as we have recently shown, the construct made from beams connected as illustrated in Fig. 1(a) can exhibit NPR since when it is uniaxially stretched, the beams will flex as illustrated in Fig. 1(b) with the net effect that the triangles rotate relative to each other to produce a more open structure (the ‘‘rotating triangles’’ effect, resulting in negative Poisson’s ratios of 1 in-plane if the triangles are equilateral. In such systems, the straight beams of length 2l can either be welded together or connected through the use of ‘‘pin joint’’-type connections at ends and centres of the beams (corresponding to the vertices of the triangles) where the axes of the ‘‘pin joints’’ are orthogonal to the plane of the structure. The use of such ‘‘pin joints’’ is possible since the formation of the triangles reduces the degrees of freedom of the system and give the structure its characteristic shear rigidity. The presence of these triangles also provide us with a route for turning this auxetic structure into one which can also exhibit negative thermal expansion since as recently proposed, equilateral triangles constructed in such a way that their base is made from a material with a thermal expansion coefficient being at least four times that of the other two sides will get shorter when heated (the ‘‘shortening of triangles’’ mechanism). In fact, it has been shown that dh, the change in height h when the equilateral triangle in Fig. 2 is subjected to a temperature change dT is given by:

After more than 20 years of development, metamaterials have gradually become an important subject in new material technology since their birth in the early century. As an important part of modern metamaterials, materials with negative Poisson's ratio have been applied in aerospace, military industry, medical and health care, satellite, automobile, ship, transportation and packaging and other fields ^[1-5]. In this paper, a three-dimensional negative Poisson's ratio structure is designed, and the influence of its structural parameters on mechanical properties is studied through theoretical calculation and simulation. The negative Poisson's ratio performance of three-dimensional negative Poisson's ratio structure in multiple directions makes it promising to be applied in a variety of occasions.

The weak stiffness and strength of materials with negative Poisson’s ratio limits their application. In this paper, three types of novel lattices with negative Poisson’s ratio are proposed to improve not only stiffness and strength but also energy absorption capacity by embedding different ribs into a classic re-entrant structure. Unit cell analyses show these novel lattices have significantly increased Young’s modulus along the loading direction, and Type C can maintain sufficient negative Poisson’s ratio performance compared with the base lattice. In addition, the novel lattices exhibit higher yield stress, plateau stress and densification strain extracted from quasi-static compressive simulation. The lattices are prototyped by laser-based additive manufacturing and tested in quasi-static experiments, which show the experimental data match the numerical results within an error of margin. The work signifies the prospect of lattices with negative Poisson’s ratio in enhancing engineering-applicable structures, and indicates the potential of structural topology optimization in more sophisticated designs.

Materials exhibiting a negative Poisson’s ratio have garnered considerable attention due to the improved toughness, shear resistance, and vibration absorption properties commonly found in auxetic materials. In this work, the nonlinear effect on the Poisson’s ratio was derived theoretically and verified by first-principle calculations and molecular dynamics simulations of two-dimensional nanomaterials including graphene and hexagonal boron nitride. The analytic formula explicitly shows that the Poisson’s ratio depends on the applied strain and can be negative for large applied strains, owing to the nonlinear interaction. Both first-principle calculations and molecular dynamics simulations show that the nonlinear effect is highly anisotropic for graphene, where the nonlinearity-induced negative Poisson’s ratio is much stronger for the strain applied along the armchair direction. These findings provide valuable insights into the behavior of materials with negative Poisson’s ratios and emphasize the importance of considering nonlinear effects in the study of the Poisson’s ratio of two-dimensional materials.

Rutile-mimic 3D metamaterials with simultaneously negative Poisson's ratio and negative compressibility

It is feasible to design laminated composites with negative Poisson's ratio. Although the minimum value of negative Poisson's ratio design can be done via numerical approach, it is possible to use the analytical method in this paper to perform the following tasks: (a) evaluate the approximated ply orientation angles to obtain maximum transverse strain cy, (b) determine the necessary conditions of design negative Poisson's ratio, and (c) investigate the influence of laminae properties on the Poisson's ratio of a composite laminate. In this study, it is also found that, in general, the ply orientations for obtaining maximum transverse strain, sy, in a composite laminate are close to 70'/20I%.

Poisson’s ratio is one of the fundamental features of materials, reflecting the transverse strain response to the applied certain axial strain. The materials with a negative Poisson’s ratio, also known as auxetic materials, are rare in nature and attract lots of research interest because of their unusual mechanical behavior and extensive applications in mechanical nanodevices. Here, we proposed and studied a novel hyperbolic two-dimensional graphene-like structure (GLS) showing a negative Poisson’s ratio behavior by first-principles calculation. The thermodynamic, dynamic, lattice dynamic, and mechanical stabilities of the GLS were carefully studied. In addition, we also explored the electronic structure, mechanical characteristics, and optical-electronic characteristics. The GLS not only displays a negative Poisson’s ratio in certain directions but also shows low-gap semiconductor characteristics and superior electronic conductivity. It is a potential sunscreen material because of the outstanding reflection and absorption for ultraviolet and infrared light.

The Poisson's ratio of a material characterizes its response to uniaxial strain. Materials normally possess a positive Poisson's ratio - they contract laterally when stretched, and expand laterally when compressed. A negative Poisson's ratio is theoretically permissible but has not, with few exceptions of man-made bulk structures, been experimentally observed in any natural materials. Here, we show that the negative Poisson's ratio exists in the low-dimensional natural material black phosphorus and that our experimental observations are consistent with first-principles simulations. Through applying uniaxial strain along armchair direction, we have succeeded in demonstrating a cross-plane interlayer negative Poisson's ratio on black phosphorus for the first time. Meanwhile, our results support the existence of a cross-plane intralayer negative Poisson's ratio in the constituent phosphorene layers under uniaxial deformation along the zigzag axis, which is in line with a previous theoretical prediction. The phenomenon originates from the puckered structure of its in-plane lattice, together with coupled hinge-like bonding configurations.

In this paper, a novel three‐dimensional (3D) cellular structure with negative Poisson's ratio was designed by alternating cuboid surface indents on the vertical ribs of the unit cells. The Poisson's ratio and Young's modulus of structures with different geometric parameters were determined using the finite element method (FEM) as a function of these parameters. Samples with identical geometric variables were fabricated via 3D printing, and their through‐thickness direction Poisson's ratios were measured and compared with simulation results. Results showed that the Poisson's ratio of the 3D cellular structures can be tuned from positive to negative and can reach a minimal value of −0.958. Good agreement was found between the experimental results and the simulation. This lattice structure is considerably stiffer than re‐entrant negative Poisson's ratio foam with the same solid phase. The design concept developed here can be optimized for specific applications via geometric parameters manipulation.

A novel two-dimensional C36 fullerene network; an isotropic, auxetic semiconductor with low thermal conductivity and remarkable stiffness

Estimation of effective properties of composite sandwich panels with negative Poisson's ratio by using variational asymptotic multiscale method

The negative Poisson's ratio (NPR) effect usually endows materials with promising ductility and shear resistance, facilitating a wider range of applications. It has been generally acknowledged that alloys show strong advantages in manipulating material properties. Thus, a thought-provoking question arises: how does alloying affect the NPR? In this paper, based on first-principles calculations, we systematically study the NPR in two-dimensional (2D) GaN and AlN, and their alloy of AlxGa1-xN. It is intriguing to find that the NPR in AlxGa1-xN is significantly enhanced compared to the parent materials of GaN and AlN. The underlying mechanism mainly originates from a counter-intuitive increase of the bond angle θ. We further study the microscopic origin of the anomalies by electron orbital analysis as well as electron localization functions. It is revealed that the distribution and movement of electrons change with the applied strain, providing a fundamental view on the effect of strain on lattice parameters and the NPR. The physical origin as revealed in this study deepens the understanding of the NPR and shed light on the future design of modern nanoscale electromechanical devices with fantastic functions based on the auxetic nanomaterials and nanostructures.

Controlling stress and deformation induced by thermo-mechanical stimulation in high-precision mechanical systems can be achieved by mechanical metamaterials (MM) exhibiting negative thermal expansion (NTE) and negative Poisson's ratio (NPR). However, the inverse design of MM exhibiting a wide range of arbitrary target NTEs and NPRs is a challenging task due to the low design flexibility of analytical methods and parametric studies based on numerical simulation. In this study, we propose Bézier curve-based programmable chiral mechanical metamaterials (BPCMs) and a deep autoencoder-based inverse design model (DAIM) for the inverse design of BPCMs. Through iterative transfer learning with data augmentation, DAIM can generate BPCMs with a curved rib shape inaccessible with the Bézier curve, which improves the inverse design performance of the DAIM in the data sparse domain. This approach decreases the mean absolute error of NTE and NPR between the inverse design target and the numerical simulation results of inverse designed BPCMs on the data-sparse domain by 79.25% and 83.33% on average, respectively. A 3D-printed BPCM is validated experimentally and exhibits good coincidence with the target NTE and NPR. Our proposed BPCM and the corresponding inverse design framework enable the inverse design of BPCMs with NTE in the range of -1100 to 0 ppm K-1 and NPR in the range of -0.6 to -0.1. Furthermore, programmable thermal deformation modes with a fixed Poisson's ratio are realized by combining various inverse designed BPCM unit cells. BPCMs and the DAIM for their inverse design are expected to improve the mechanical robustness of high-precision mechanical systems through tunable modulation of thermo-mechanical stimulation.

Nacre, known for its brick-and-mortar structure consisting of 95% aragonite and 5% organic matrix, exhibits auxetic behaviour, as shown through experimental analyses. The auxeticity of nacre is still widely unexplored, with no conclusive answer as to the mechanism causing this unexpected property. This project aims to investigate the speculative theories on the mechanisms causing the auxeticity of nacre and further look into how the negative Poisson’s ratio (NPR) can be enhanced. This project utilises analytical and numerical modelling to create and optimise nacre-inspired mechanical metamaterial with negative Poisson’s ratio. The focus of the models was to explore the mechanisms that could explain nacre’s auxeticity but also to find the correlation between Poisson’s ratio (PR) and the geometrical parameters. Four different models were presented in the literature review, and three of them were further modelled. Focus was given to mechanism 1, which speculated on the role of the mortar in the nacre's auxeticity. Mechanisms 2 and 3 were explored and investigated the role of brick morphology and connectivity. Analyses of mechanism 1 revealed dependencies of PR on volume ratio (the ratio of volume of bricks and mortar) and geometry, indicating that higher volume ratio models had lower PR but were prone to experienced yielding at lower strains. Combined bending and axial deformation of the struts in the X-shaped mortar was identified as a significant factor in the NPR of the 2D model of mechanism 1. The 2D numerical model of mechanism 1 exhibited the same behaviour pattern as nacre but with lower PR, signifying the model’s validity and making it a good contender for an explanation of nacre’s auxetic behaviour. Mechanism 1 was then explored as a 3D numerical model. The 3D models showed altered deformation mechanisms and NPR behaviour. It was recognised that the depth of the 3D models prevented the structures from showing the same behaviours as 2D models. The structure was not slender enough to experience the same type of deformation. The out-of-plane deformation was thought to be another contributing factor. To rectify this, a thin structure with beam elements was created. The beam 3D structure showed similar variability of PR as the 2D models, but no exact match was found. The lowest PR achieved through numerical modelling of mechanism 1 was during the 2D analysis showing a PR of approximately -0.80 for the volume ratio of 0.91. The project underscores the significance of understanding geometric properties and deformation behaviours in auxetic materials, providing insights into optimising NPR in nacre-inspired mechanical metamaterials.