СВОЙСТВА КРИВЫХ ОБЪЕМНОЙ, ОСЕВОЙ И ПОПЕРЕЧНОЙ ПОЛЗУЧЕСТИ ПРИ ОДНООСНОМ РАСТЯЖЕНИИ, ПОРОЖДАЕМЫХ НЕЛИНЕЙНЫМ СООТНОШЕНИЕМ ВЯЗКОУПРУГОСТИ РАБОТНОВА

The Boltzmann–Volterra linear constitutive equation for isotropic non-aging viscoelastic materials (with an arbitrary shear and bulk creep compliances) is studied analytically in order to find out its capabilities to provide an adequate qualitative description of rheological phenomena related to creep under uni-axial loading and types of evolution of the Poisson’s ratio (lateral contraction ratio in creep) and to outline the control scopes of the material functions . The constitutive equation doesn’t involve the third invariants of stress and strain tensors (or the Lode–Nadai coefficients) and implies that their hydrostatic and deviatoric parts don’t depend on each other. It is controlled by two material functions of a positive real argument (that is shear creep compliance and bulk creep compliance); they are implied to be positive, differentiable, increasing and convex functions. General properties of the creep curves for volumetric, longitudinal and lateral strain generated by the model under uni-axial loading are studied. Conditions for creep curves monotonicity and for existence of extrema and sign changes of strains and the Poisson’s ratio evolution in time are studied. The influence of qualitative restrictions imposed on its material functions is analyzed. The expressions for Poisson’s ratio through the strain triaxiality ratio and in terms of creep compliances are derived. Assuming creep compliances are arbitrary (permissible), general accurate two-sided bounds for the Poisson’s ratio range are obtained; it is proved that the lateral contraction ratio in creep is greater than –1 and less than 0,5 at any moment of time. Additional restrictions on material functions and stress levels are derived to provide negative values of Poisson’s ratio. Criteria for the Poisson’s ratio increase or decrease and for its non-dependence on time are found. In particular, it is proved that the linear relation is able to simulate non-monotonic behavior and sign changes of lateral strain and Poisson’s ratio under constant axial load

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 with a negative Poisson's ratio, also known as auxetics, have attracted a lot attention as they have shown innovation potential in applications for energy damping, modern fasteners, biomedical implants, piezoelectric sensors, and soft actuators. In this study, we introduce different patterns of graded distribution of unit cells with positive and negative Poisson's ratio in tubular configurations. Seven types of patterns are programmed into the fabric of the metamaterial to create desired shape changes upon applying far-field external loads. Two of the patterns demonstrate near-zero Poisson's ratio even at axial strains as high as 44%. Other pattern distributions convert the initially cylindrical shape of the tubes to vase, barrel, hourglass, nonsymmetrical vase, and nonsymmetrical hourglass geometries. The experimental Poisson's ratio values for the linear negative-to-positive-to-negative gradient (resulting in hourglass shape) and linear positive-to-negative-to-positive gradient (resulting in barrel shape) cases are +0.53 and −0.47, respectively. The measured Poisson's ratio values at tube level are in good accordance with the analytical values of +0.5 and −0.5. Benefits of the proposed designs in applications such as action-at-a-distance actuators and wrinkle-free jointless hinges in both 3D and 2D configurations are demonstrated.

Auxetic yarn was successfully produced by a wrap filament and a core filament based on a ring-spinning system, which showed an auxetic effect when stretched, that is, expanding transversely under tension. Yarns were spun by different structural parameters of the core filament and the wrap filament, including diameter ratio, helical angle and tensile modulus of the wrap filament. Corresponding tensile tests were utilized to analyze the effects of structural parameters and performance on outer contour deformation of auxetic yarn. Experimental results showed that the outer contour of auxetic yarn expanded transversely under tension and there existed significant negative Poisson's ratio values in the Poisson's ratio-strain curve, and it was found that the auxetic effect became more observable with a higher diameter ratio of the core filament to the wrap filament, and lower helical angle and larger tensile modulus of the wrap filament. Moreover, compared with theoretical results by theoretical modeling in Part I, good relations of Poisson's ratio-strain curves were obtained between experimental and theoretical results. This proves the effectiveness of spinning auxetic yarn by selecting reasonable components of yarn and it is feasible to design yarn with a negative Poisson's ratio effect.

In this paper the static and dynamic performances of sandwich structures with in-plane negative Poisson's ratio core are investigated from an analytical point of view. The cellular material theory is applied to calculate the orthotropic mechanical properties of re-entrant cell honeycomb cores which shows negative Poisson's ratio values. This special geometrical layout of the cells allows an higher out-of-plane shear modulus compared to the one of regular honeycombs. The laminate orthotropic plate theory with shear correction factors is applied in order to describe the static and dynamic behaviour of symmetric sandwich plates with different core to sheet thickness ratios. Comparisons are made with analogous structures with regular honeycomb. The maximum deflections due to uniform pressure and buckling loads are enhanced, while the natural frequencies show a slight enhancing for some parameters of the cells.

We describe a new class of negative Poisson's ratio (NPR) open cell PU-PE foams produced by blocking the shape memory effect in the polymer. Contrary to classical NPR open cell thermoset and thermoplastic foams that return to their auxetic phase after reheating (and therefore limit their use in technological applications), this new class of cellular solids has a permanent negative Poisson's ratio behavior, generated through multiple shape memory (mSM) treatments that lead to a fixity of the topology of the cell foam. The mSM-NPR foams have Poisson's ratio values similar to the auxetic foams prior their return to the conventional phase, but compressive stress-strain curves similar to the ones of conventional foams. The results show that by manipulating the shape memory effect in polymer microstructures it is possible to obtain new classes of materials with unusual deformation mechanisms.

Recently, mechanical metamaterials have garnered extensive interests due to their unique properties. By combining hierarchical structures with the concept of size effect, mechanical metamaterials have enabled the creation of a sequence of novel designs. Those new materials allow us to explore new regions in the materials space, including ultrahigh resilience, high strength-to-volume, strong energy absorption, negative thermal expansion and so on. One of the most interesting properties of mechanical metamaterials is the negative Poisson's ratio.Poisson's ratio is the ratio of transverse contraction strain to longitudinal extension strain in the direction of stretching force. In most cases, Poisson's ratio is positive, which means that as a material is stretched along the lateral direction, it becomes thinner along the transverse direction. In contrast, the thickness of a material with a negative Poisson's ratio increases when it is stretched. A range of natural and artificial materials, including certain polymers, metals, and ceramics, exhibit this so-called auxetic characteristic. Materials with negative Poisson's ratio offer special mechanical and thermal characteristics that are advantageous for a variety of applications, such as energy absorption, sensing, and medical implants. Auxetic materials also exhibit mechanical properties that are unique compared to conventional materials including indentation resistance, shear resistance and fracture resistance. In my thesis work, I have explored four kinds of auxetic designs with interesting properties. The designs in my study include re-entrant ribs and a star shape, both of which exhibit good auxetic behaviors. Two of the designs also demonstrate auxetic behaviors in both directions. I have used stereolithography to fabricate the samples and applied tension test to measure their mechanical properties. The experimental results confirm that all four structures exhibit auxetic characteristics, and the re-entrant ribs and star-shape structures can enhance the auxetic behavior. --Author's abstract

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:

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%.

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.

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.

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.

Three-dimensional metamaterials exhibiting extreme isotropy and negative Poisson's ratio

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