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Auxetic materials differ from conventional materials by the manner in which they respond to stretching; they tend to get fatter when stretched, resulting in a negative Poisson's ratio. The purpose of this paper is to present a numerical methodology for design of microstructure of 2D and 3D auxetic materials with a wide range of different negative Poisson's ratios.

The proposed methodology is based on a combination of finite element method and a genetic algorithm. The problem is formulated as an optimization problem of finding microstructures with prescribed behavioral requirements. Different microstructures are generated and evolved using the genetic algorithm and the behavior of each microstructure is analyzed using the finite element method to evaluate its fitness in competition with other generated structures.

Numerical examples show that it is possible to design a large number of new auxetic materials, each with a different value of negative Poisson's ratio.

The proposed methodology can be used as an effective method to tailor new materials with prescribed values of negative (or positive) Poisson's ratio. The methodology can also be used to optimize other material properties.

To investigate the relation between the Poisson's ratio of a re‐entrant honeycomb structure by varying the micropolar material constants such as micropolar Young's modulus E_m, micropolar Poisson's ratio V_m, characteristic length l, coupling factor N, and micropolar elastic constants in accordance with the micropolar elastic restrictions, a 2‐D triangular finite element formulation including an extra degree of freedom was derived on the basis of Eringen's micropolar elasticity theory by using a linear triangular element. The effects on the structural Poisson's ratio of the honeycomb structure are studied in detail.

Negative Poisson’s ratio (NPR) material has huge potential applications in various industrial fields. However, lower Young’s modulus due to the porous form limits its further applications. Based on the topology optimization technique, this paper aims to optimize the structure consisting two isotropic porous materials with positive Poisson’s ratio (PPR) and NPR and void.

Under prescribed dual-volume fraction constraints, the structural compliance is taken as the objective. Young’s modulus and Poisson’s ratio are, respectively, interpolated and expressed with Lamé’s parameters for easier programming. Accordingly, the sensitivities can be derived through the chain rule. Several two- and three-dimensional illustrative examples are presented to demonstrate the capability and effectiveness of the proposed approach. The influences of Poisson’s ratios, volume fractions and Young’s moduli on the optimized results are investigated.

For NPR materials having unique load responses, the resulting topologies of PPR and NPR materials have distinct material distributions in comparison of the results from two PPR materials. Furthermore, it is observed that higher structural stiffness can be achieved from the hybrid of PPR and NPR materials than that obtained from the structures made of individual constituent materials.

A topology optimization methodology is proposed to design structures composed of PPR and NPR materials.

Based on Eringen’s micropolar elasticity theory (MET), a two‐dimensional finite element formulation including one extra degree of freedom is derived by using a linear triangular element, and a corresponding computer program is also developed. By varying the technical constants such as micropolar Young’s modulus E_m, micropolar Poisson’s ratio ν_m, characteristic length l, coupling factor N, and micropolar elastic constants in accordance with the micropolar elastic restrictions, their effects on the Poisson’s ratio of the rectangular plate are studied in detail.

The “chiralisation” of Euclidean polygonal tessellations is a novel, recent method which has been used to design new auxetic metamaterials with complex topologies and improved geometric versatility over traditional chiral honeycombs. This paper aims to design and manufacture chiral honeycombs representative of four distinct classes of 2D Euclidean tessellations with hexagonal rotational symmetry using fused-deposition additive manufacturing and experimentally analysed the mechanical properties and failure modes of these metamaterials.

Finite Element simulations were also used to study the high-strain compressive performance of these systems under both periodic boundary conditions and realistic, finite conditions. Experimental uniaxial compressive loading tests were applied to additively manufactured prototypes and digital image correlation was used to measure the Poisson’s ratio and analyse the deformation behaviour of these systems.

The results obtained demonstrate that these systems have the ability to exhibit a wide range of Poisson’s ratios (positive, quasi-zero and negative values) and stiffnesses as well as unusual failure modes characterised by a sequential layer-by-layer collapse of specific, non-adjacent ligaments. These findings provide useful insights on the mechanical properties and deformation behaviours of this new class of metamaterials and indicate that these chiral honeycombs could potentially possess anomalous characteristics which are not commonly found in traditional chiral metamaterials based on regular monohedral tilings.

To the best of the authors’ knowledge, the authors have analysed for the first time the high strain behaviour and failure modes of chiral metamaterials based on Euclidean multi-polygonal tessellations.

Auxetic sandwich structures are gaining attention because of the negative Poisson’s ratio effect offered by these structures. Re-entrant core was one configuration of the auxetic structures. There is a growing concern about the design and behavior of re-entrant cores in aerospace, marine and protection applications. Several researchers proposed various designs of re-entrant core sandwiches with various materials. The purpose of this study is to review the most recent advances in re-entrant core sandwich structures. This review serves as a guide for researchers conducting further research in this wide field of study.

The re-entrant core sandwich structures were reviewed in terms of their design improvements, impact and quasi-static crushing responses. Several design improvements were reviewed including 2D cell, 3D cell, gradient, hierarchical and hybrid configurations. Some common applications of the re-entrant core sandwiches were given at the end of this paper with suggestions for future developments in this field.

Generally, the re-entrant configuration showed improved energy absorption and impact response among auxetic structures. The main manufacturing method for re-entrant core manufacturing was additive manufacturing. The negative Poisson’s ratio effect of the re-entrant core provided a wide area of research.

Generally, re-entrant cores were mentioned in the review articles as part of other auxetic structures. However, in this review, the focus was solely made on the re-entrant core sandwiches with their mechanics.

The purpose of this paper is to study the effect of the relative density and geometric parameters on the homogenised in-plane elasticity modulus of a cellular honeycomb structure using analytical and numerical approaches.

In this work, the mechanical behaviour of a new design of the honeycomb is analysed through a refined analytical model that is developed based on the energy theorems by considering the shearing and stretching effects in addition to bending.

By taking into account the various deformation mechanisms (MNT), the obtained results show that the values of elasticity modulus are the same for low relative densities, but the difference becomes remarkable for higher densities. Moreover, it is difficult to judge the effect of the relative density and anisotropy of the cellular structure on the values of the homogenised elasticity modulus without considering all the three deformation mechanisms in the analytical model. It is shown that conventional models overestimate the elasticity modulus, especially for high relative densities.

In this paper, a refined model that takes into account the three deformation mechanisms (MNT) is developed to predict the in-plane elasticity modulus of a honeycomb cellular material. It is shown that analytical models that describe the anisotropic behaviour of honeycomb cells can be improved by considering the three deformation mechanisms, which are bending, stretching, and shearing deformations.

The purpose of this study is to introduce a new concept in engineered materials and that is truss substructured materials (TSMs). These materials would be engineered to express mechanical abilities that are seldom found in nature.

This article starts with defining TSMs and how to classify and name TSMs. The article also introduces the theoretical modeling of TSMs, the software developed for analyzing TSMs and the parametric studies performed.

After these studies, new materials are introduced that have abilities such as negative Poisson ratio in X and Y direction, negative Poisson ratio in one direction (either x or y), self-remodeling under stress.

The research is done in 2D, further studies in 3D using 3D printing are required to make the suggested materials a viable real-world solution.

The main contribution of this research work is the proposed nomenclature that creates a system for researchers to experiment and create novel and unique versions of the proposed materials. Furthermore, some of the materials developed exhibit some unique properties that may create advances in engineering with further development.

The present paper aims at the multi-objective optimization of a reentrant hexagonal cell auxetic structure. In addition, a parametric analysis will be carried out to verify how each of the design factors impact each of the responses.

The multi-objective optimization of five different responses of an auxetic model was considered: mass, critical buckling load under compression effort, natural frequency, Poisson's ratio and failure load. The response surface methodology was applied, and a new meta-heuristic of optimization called the multi-objective Lichtenberg algorithm was applied to find the optimized configuration of the model. It was possible to increase the failure load by 26.75% in compression performance optimization. Furthermore, in the optimization of modal performance, it was possible to increase the natural frequency by 37.43%. Finally, all 5 responses analyzed simultaneously were optimized. In this case, it was possible to increase the critical buckling load by 42.55%, the failure load by 28.70% and reduce the mass and Poisson's ratio by 15.97 and 11%, respectively. This paper addresses something new in the scientific world to date when evaluating in a multi-objective optimization problem, the compression and modal performance of an auxetic reentrant model.

It was possible to find multi-objective optimized structures. It was possible to increase the critical buckling load by 42.82%, and the failure load in compression performance by 26.75%. Furthermore, in the optimization of modal performance, it was possible to increase the natural frequency by 37.43%, and decrease the mass by 15.97%. Finally, all 5 responses analyzed simultaneously were optimized. In this case, it was possible to increase the critical buckling load by 42.55%, increase the failure load by 28.70% and reduce the mass and Poisson's ratio by 15.97 and 11%, respectively.

There is no work in the literature to date that performed the optimization of 5 responses simultaneously of a reentrant hexagonal cell auxetic structure. This paper also presents an unprecedented statistical analysis in the literature that verifies how the design factors impact each of the responses.

This paper aims to study the tensile performance, deformation characteristics, auxeticity and stability of different auxetic tubular structures generated by cutting method and pattern scale factor (PSF) method using validated finite element analysis.

Two types of auxetic tubular structures were designed by a coordinate transformation method and the PSF adjustment method, respectively. ABAQUS/explicit solver was used for the large deformation analysis and the displacement of key nodes was extracted to calculate Poisson’s ratio value and evaluate the deformation of tubular structures.

The random cut method was not suitable for designing auxetic tubular structures. Vertical and horizontal cut approach was suitable, but the change of the tubular diameter was lower than the tubular structures generated by the PSF adjustment method.

Simple ways to generate auxetic tubular structure, which can be made into intelligent and foldable equipment, such as annuloplasty rings, angioplasty stents and oesophageal stents. By combined with shape memory polymer, various smart tubular materials and structures with various functions can be designed, especially in medical scaffold and other medical equipment fields.

The auxetic characteristic of tubular structure designed by using random cut method has been investigated for the first time. The outcome of this study would be very useful design tubular structures with better mechanical properties.