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Auxetic materials are a kind of non-conventional materials having negative Poisson’s ratio. They laterally expand when stretched or laterally shrink when compressed. Compared to conventional materials, auxetic materials have a number of enhanced properties that could be very interesting for some special applications. This paper reviews the latest achievements in auxetic materials, including their properties, structures and applications. A special discussion on their potential applications in textiles is also made. It is expected that this review could provide some useful information for the future development of auxetic textile materials.

Auxetic materials exhibit a negative Poisson’s ratio, i.e., they become thicker rather than thinner in at least one dimension when strained. Recently, a nematic liquid crystal elastomer (LCE) was shown to be the first synthetic auxetic material at a molecular level. Understanding the mechanism of the auxetic response in LCEs is clearly important, and it has been suggested through detailed Raman scattering studies that it is related to the reduction of uniaxial order and emergence of biaxial order on strain. In this paper, we demonstrate direct observation of the biaxial order in an auxetic LCE under strain. We fabricated ~100 μm thick LCE strips with complementary geometries, exhibiting either planar or homeotropic alignment, in which the auxetic response is seen in the thickness or width of the sample, respectively. Polarized Raman scattering measurements on the planar sample show directly the reduction in the uniaxial order parameters on strain and suggest the emergence of biaxial order to mediate the auxetic response in the sample thickness. The homeotropic sample is studied via conoscopy, allowing direct observation of both the auxetic response in the width of the sample and increasing biaxiality in the LCE as it is strained. We verified that the mechanism of the auxetic response in auxetic LCEs is due to the emergence of the biaxial order and conclude such materials can be added to the small number of biaxial nematic systems that have been observed. Importantly, we also show that the mechanical Frèedericksz transition seen in some LCEs is consistent with a strain-induced transition from an optically positive to an optically negative biaxial system under strain, rather than a director rotation in a uniaxial system.

This work proposes the complete design cycle for several auxetic materials where the cycle consists of three steps (i) the design of the micro-architecture, (ii) the manufacturing of the material and (iii) the testing of the material. We use topology optimization via a level-set method and asymptotic homogenization to obtain periodic micro-architectured materials with a prescribed effective elasticity tensor and Poisson’s ratio. The space of admissible micro-architectural shapes that carries orthotropic material symmetry allows to attain shapes with an effective Poisson’s ratio below -1. Moreover, the specimens were manufactured using a commercial stereolithography Ember printer and are mechanically tested. The observed displacement and strain fields during tensile testing obtained by digital image correlation match the predictions from the finite element simulations and demonstrate the efficiency of the design cycle.

The durability improvement of mechanical systems produced by Additive Manufacturing has become a key challenge in the industry, especially with architectured materials which present enhanced physical properties. Additive Manufacturing has also made it possible to develop architectured materials which are cellular or distributed materials in which the topological allocation is controlled and optimized for specific functions or properties, such as auxetic materials. Auxetics are structures that have a negative Poisson’s ratio which becomes thicker perpendicular to the applied tensile force. Moreover, Generative Design is a design exploration process to create highly optimized design making additive technology one of the best ways to access some new design space. This work aims to combine Generative Design and Integrated Design as part of a simultaneous approach to evaluate the capabilities of auxetic materials made by Fused Filament Fabrication in 3D printing. Three main aspects are considered in this approach: the parametric design of a pattern geometry to generate a structured part considering fabrication constraints through design guidelines, the additive manufacturing of the generated part and the evaluation of the structured material’s mechanical behavior. Three-point bending tests are also carried out to validate the analytical approach as well as to study auxetic structures properties. This parametric design methodology allowed for the fabrication of auxetic bending specimens. Outcomes from mechanical tests were used to elaborate an equivalent simplified beam model to predict the elastic behavior of auxetic materials before manufacturing. Then, the mechanical tests have shown also that the pattern’s compression around stress application aims to reinforce the structure. The results show the potential of the implemented global and simultaneous approach to develop auxetic materials through a Generative Design for Additive Manufacturing methodology. Hence, this research work provides a basis for further work to improve the numerical analysis aspect and extend the approach to develop architectured and functionalized materials. The results show multiple auxetic design iterations of bending specimens based on geometric, material, and additive technology parameters in order to verify their mechanical behaviors.

A generalized strain energy-based homogenization method for 2-D and 3-D cellular materials with and without periodicity constraints is proposed using Hill’s Lemma and the matrix method for spatial frames. In this new approach, the equilibrium equations are enforced at all boundary and interior nodes and each interior node is allowed to translate and rotate freely, which differ from existing methods where the equilibrium conditions are imposed only at the boundary nodes. The newly formulated homogenization method can be applied to cellular materials with or without symmetry. To illustrate the new method, four examples are studied: two for a 2-D cellular material and two for a 3-D pentamode metamaterial, with and without periodic constraints in each group. For the 2-D cellular material, an asymmetric microstructure with or without periodicity constraints is analyzed, and closed-form expressions of the effective stiffness components are obtained in both cases. For the 3-D pentamode metamaterial, a primitive diamond-shaped unit cell with or without periodicity constraints is considered. In each of these 3-D cases, two different representative cells in two orientations are examined. The homogenization analysis reveals that the pentamode metamaterial exhibits the cubic symmetry based on one representative cell, with the effective Poisson’s ratio v¯ being nearly 0.5. Moreover, it is revealed that the pentamode metamaterial with the cubic symmetry can be tailored to be a rubber-like material (with v¯ ≅0.5) or an auxetic material (with v¯ < 0).

In this study, a new technique is presented for enhancing the vibration suppression of shunted piezoelectrics by using an auxetic composite layer. Finite element models have been created to simulate the dynamic behavior of the piezoelectric composite beam. In particular, 2D FE and 3D FE models have been created by simulating the shunt as a passive controller and their results are compared. Furthermore, a parametric analysis is presented of the circuit elements, i.e., the resistors, inductors, and capacitors and of the auxetic material, i.e., the thickness. It was found that the proposed modification by adding an auxetic layer of a considerable thickness enhances the electromechanical coupling and indirectly influences the vibration control of the whole structure. However, the use of 3D modeling is necessary to study this auxetic enhancement.

Recent theoretical work suggests that systematic pruning of disordered networks consisting of nodes connected by springs can lead to materials that exhibit a host of unusual mechanical properties. In particular, global properties such as Poisson’s ratio or local responses related to deformation can be precisely altered. Tunable mechanical responses would be useful in areas ranging from impact mitigation to robotics and, more generally, for creation of metamaterials with engineered properties. However, experimental attempts to create auxetic materials based on pruning-based theoretical ideas have not been successful. Here we introduce a more realistic model of the networks, which incorporates angle-bending forces and the appropriate experimental boundary conditions. A sequential pruning strategy of select bonds in this model is then devised and implemented that enables engineering of specific mechanical behaviors upon deformation, both in the linear and in the nonlinear regimes. In particular, it is shown that Poisson’s ratio can be tuned to arbitrary values. The model and concepts discussed here are validated by preparing physical realizations of the networks designed in this manner, which are produced by laser cutting 2D sheets and are found to behave as predicted. Furthermore, by relying on optimization algorithms, we exploit the networks’ susceptibility to tuning to design networks that possess a distribution of stiffer and more compliant bonds and whose auxetic behavior is even greater than that of homogeneous networks. Taken together, the findings reported here serve to establish that pruned networks represent a promising platform for the creation of unique mechanical metamaterials.

Auxetic materials expand in an unusual way: perpendicular to the direction in which they are stretched. Lipton et al. engineered a type of auxetic material that also has handedness. When this material is sheared, it twists either to the right or the left. By tiling the underlying patterns onto spheres and cylinders, rigid or compliant structures can be made. Linear and 4-degree-of-freedom actuators can thus be made from hollow tubes, which could be valuable for a variety of engineering and medical applications. Science , this issue p. 632 Translating two-dimensional auxetic tilings to spheres and cylinders allows engineering of rigid or compliant structures. In nature, repeated base units produce handed structures that selectively bond to make rigid or compliant materials. Auxetic tilings are scale-independent frameworks made from repeated unit cells that expand under tension. We discovered how to produce handedness in auxetic unit cells that shear as they expand by changing the symmetries and alignments of auxetic tilings. Using the symmetry and alignment rules that we developed, we made handed shearing auxetics that tile planes, cylinders, and spheres. By compositing the handed shearing auxetics in a manner inspired by keratin and collagen, we produce both compliant structures that expand while twisting and deployable structures that can rigidly lock. This work opens up new possibilities in designing chemical frameworks, medical devices like stents, robotic systems, and deployable engineering structures.

Background Today, energy harvesting is a hot topic in the scientific community because of the scarcity and insufficiency of energy resources. Piezoelectric systems have been proven by many studies to be very efficient in energy harvesting. In addition, an increase in efficiency has been observed by using auxetic materials in piezoelectric systems due to their extraordinary properties. Because of its capability to sustainably provide wireless sensors and portable electronic devices, a worldwide effort is being made to capture energy using the mechanical vibrations of the environment. Purpose The main purpose was to understand auxetic materials and piezoelectric systems more clearly by making a comprehensive compilation. Methods This review article investigated an auxetic piezoelectric energy harvester (APEH) system focusing on the structure of auxetic materials along with their behavior and efficiency in the system. Results As a result of general examinations, it was seen that structures with negative Poisson ratios were much more efficient in energy harvesting in this type of system compared to conventional structures. Conclusion Due to APEH’s advantages such as simplicity, scalability, and high-power production, piezoelectric energy harvesting has gained more popularity than other vibration-based energy harvesting methods.

Auxetic materials exhibit a negative Poisson’s ratio under tension or compression, and such counter-intuitive behavior leads to enhanced mechanical properties such as shear resistance, impact resistance, and shape adaptability. Auxetic materials with these excellent properties show great potential applications in personal protection, medical health, sensing equipment, and other fields. However, there are still many limitations in them, from laboratory research to real applications. There have been many reported studies applying auxetic materials or structures to the development of sensing devices in anticipation of improving sensitivity. This review mainly focuses on the use of auxetic materials or auxetic structures in sensors, providing a broad review of auxetic-based sensing devices. The material selection, structure design, preparation method, sensing mechanism, and sensing performance are introduced. In addition, we explore the relationship between the auxetic mechanism and the sensing performance and summarize how the auxetic behavior enhances the sensitivity. Furthermore, potential applications of sensors based on the auxetic mechanism are discussed, and the remaining challenges and future research directions are suggested. This review may help to promote further research and application of auxetic sensing devices.