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AbstractAuxetics have emerged recently as an exciting class of mechanical metamaterials that are identified by negative Poisson’s ratio. The mechanical properties of rationally designed auxetic metamaterials are mostly influenced by their topological characteristics rather than the material properties of their constituent material. The goal of this paper is to use optimization algorithms to achieve the desired target mechanical properties for reentrant auxetic metamaterials. The GEKKO optimization package in Python is used for optimizing the geometry of auxetic lattice structures. Several mechanical properties including Poisson’s ratio, relative Young’s modulus, relative yield stress, and relative energy absorption capability, as well as the noted properties normalized with respect to relative density and relative Young’s modulus are chosen for being minimized or maximized. ANSYS finite element package is also implemented for validation of the results obtained from the optimization algorithm. According to the results, to achieve the maximum magnitude of Poisson’s ratio (positive and negative), the size of the unit cell in the lateral direction must be selected to be maximum and the thickness must become minimum. Moreover, to achieve the maximum value of the relative Young’s modulus or energy absorption in any direction, the size of the unit cell in that direction must be maximized. Also, to achieve the maximum amount of relative yield stress in both directions, the unit cell must have a maximum thickness and an internal angle close to zero. [ABSTRACT FROM AUTHOR]

AbstractThis paper presents an analysis of a sandwich structure featuring an auxetic core, manufactured through Vacuum Assisted Resin Transfer Molding (VARTM) using carbon-aramid hybrid fibers. The core was 3D printed with polylactic acid (PLA). Experimental testing of the structure provided results for validating a cost-effective numerical model. The response surface methodology identified results for different sandwich panel configurations, revealing that auxetic behavior depends on the core’s adopted configuration. Increasing the fiber-core contact area induces auxetic behaviors. The structure underwent optimization using the Lichtenberg algorithm, yielding models with 40.32% higher failure load, 36.36% higher natural frequency, and over 20% mass reduction. [ABSTRACT FROM AUTHOR]

The paper presents an analysis of rotating rigid unit (RRU) auxetic structures, the special property of which is negative Poisson's ratio. The crucial features of such modified structures are the well-functioning linkages of the square units at their pivot points. This ensures the stable functioning of such structures in tension or compression. The presented geometrical analysis of these auxetic structures may facilitate their adequate construction and allow one to determine the expected values of their expansion as well as the desired porosity. The results are confirmed based on the behaviour of physical models produced by the assembly of square units. The change in the dimensions of the physical models when moving from a closed to an open position is consistent with the predictions of the geometric models. By modifying the well-known 'rotating squares' model, physical structures with auxetic properties are obtained that can be utilised in industrial conditions, where a simultaneous change of linear dimensions is needed—either in compression or in tension. The assembly method may prove efficient in building such structures, given the abilities of assembly robots to regularly arrange the unit cells in lines and rows and to connect them with rings at the designated positions (evenly spaced perforations). The presented auxetic structures might find their potential application in, e.g., expansion joints or structures in which the porosity is mechanically changed, such as mesoscale structures. The tested structures subjected to high compressive forces buckle when the yield strength of the rigid unit material is exceeded. [ABSTRACT FROM AUTHOR]

This paper aims at to improve the vibration behavior of the train floor panel by the use of a cellular auxetic layer. A field measurement is performed to obtain the vibrational frequency content of the body floor moving on the tangent track. Using acceleration sensors, the vibrational response is measured on the bogie (as the input excitation) and on the floor panel (as the observation response). Finite Element modeling for the floor panel is accomplished and measurement data are used for both the input excitation and the verification of the numerical results. The floor panel is a sandwich panel containing multiple layers. In this study, the conventional wooden layer of the panel is substituted with a cellular auxetic one with a re-entrant hexagonal pattern. Then, an optimization problem is defined while the topological parameters of the auxetic layer are the design variables and the dynamic performance of the panel is the objective function. The parameter of power–mass–ratio (PMR) is defined taking the effects of both weight and dynamic response amplitude into calculation. It is found that the PMR is reduced to almost 0.6 by replacing the wooden layer with an auxetic one, and after topological optimization, it is reduced to 0.35. [ABSTRACT FROM AUTHOR]

The paper "Buckling of stretched strips" [1] , published in the year 2000, seemed to deal with a rather specific problem of buckling of thin structures. Nevertheless, it aroused quite broad interest and prompted a considerable series of further treatments. Deeper theoretical considerations and advanced applications have been published. Various specific aspects of this type of problem have been addressed in these papers. However, a general and systematic consideration of how and to what extent the Poisson's ratio affects the critical stretch of strips of different length to width ratios, L / B , was lacking. Accomplishing this task is the focus of this paper. Given the increasing use of auxetics, strips made from such materials are also being investigated. In addition, the occurrence of previously undiscovered mode transitions is shown. All results are presented in dimensionless form, which allows for fairly general usage. • Influence of Poisson ratio on buckling of stretched strips quantified and discussed. • So far unknown mode transition detected and explained. • Buckling of stretched strips made of auxetic materials – diagrams for buckling factor in dependence of Poisson ratio. [ABSTRACT FROM AUTHOR]

• The proposed design exhibits better energy absorption characteristics. • Reinforcing ligaments ensure uniform deformation and improved stability. • The proposed design maintains a constant Poisson's ratio under relatively large deformation. • The theoretical derivation is simple and applicable to other auxetic structures. The traditional anti-tetra-missing rib structure often suffers from uneven stress deformation and poor energy absorption, which limits its engineering applications. To address these limitations, this paper proposed a novel windmill-shaped auxetic structure by incorporating reinforcing ligaments into the traditional anti-tetra-missing rib structure. The incorporation of these reinforcing ligaments ensures that both the outer and inner ligaments of the windmill-shaped auxetic structure are adequately supported, leading to more uniform structural deformation and enhanced energy absorption capabilities. Further modifications, such as reducing the length of the outer and inner ligaments and increasing their thickness within a reasonable range, significantly enhance the energy absorption capacity. These findings provide a theoretical basis for the design and practical application of auxetic metamaterials. [Display omitted] [ABSTRACT FROM AUTHOR]

Mechanical metamaterials have generated considerable interest due to their unique attributes such as light weight, high strength, enhanced energy absorption, high impact, and fracture resistance. However, most of the design methodologies in literature are predominantly computational and provide limited user-insight (especially for three-dimensional designs). This paper presents an alternative two-phase design methodology for the conceptual synthesis of three-dimensional tunable mechanical metamaterials. In the first phase, we obtain a kinematically feasible conceptual topology using a building block-based design approach. In the second phase, the conceptual topology is refined using shape/size optimization to meet specific elastic properties and conform to manufacturing requirements. The building block-based approach uses a unique visualization formulation that represents the deformation behavior as 'load flow' in the constituent members. An immersive virtual reality tool is developed to mitigate the visual difficulty in the design of three-dimensional microstructures. Furthermore, the load flow formulation is used to propose a qualitative classification scheme for negative Poisson's ratio elastic metamaterials based on relative values of shear moduli and bi-axial elastic stiffnesses. The efficacy of the framework is illustrated through the design of microstructures with negative Poisson's ratios in spatial directions and the ability to achieve isotropic microstructures from a qualitative understanding of the conceptual designs. Such a framework can lead to the design of synthetic materials that have potential applications in multifunctional structures, shape morphing structures, and soft robotics. [ABSTRACT FROM AUTHOR]

A novel two-dimensional (2D) mechanical metamaterial with highly programmable mechanical response under compressive load is presented in this paper by introducing hierarchical rotating structures, in which flexible structures are used to replace the rigid part in conventional rotating rigid structures. Multi-step deformation pathways and negative Poisson's ratio were observed in in situ compression experiments and finite element simulations, suggesting that the mechanical behavior of the hierarchical metastructure is highly ordered and can be programmed by constraining angles of the proposed metamaterial. This work offers new insights to create mechanical metamaterial using hierarchical rotating structures for flexible devices and crashworthiness applications. [ABSTRACT FROM AUTHOR]

Purpose: While additive manufacturing via melt-extrusion of plastics has been around for more than several decades, its application to complex geometries has been hampered by the discretization of parts into planar layers. This requires wasted support material and introduces anisotropic weaknesses due to poor layer-to-layer adhesion. Curved-layer manufacturing has been gaining attention recently, with increasing potential to fabricate complex, low-weight structures, such as mechanical metamaterials. This paper aims to study the fabrication and mechanical characterization of non-planar lattice structures under cyclic loading. Design/methodology/approach: A mathematical approach to parametrize lattices onto Bèzier surfaces is validated and applied here to fabricate non-planar lattice samples via curved-layer fused deposition modeling. The lattice chirality, amplitude and unit cell size were varied, and the properties of the samples under cyclic-loading were studied experimentally. Findings: Overall, lattices with higher auxeticity showed less energy dissipation, attributed to their bending-deformation mechanism. Additionally, bistability was eliminated with increasing auxeticity, reinforcing the conclusion of bending-dominated behavior. The analysis presented here demonstrates that mechanical metamaterial lattices such as auxetics can be explored experimentally for complex geometries where traditional methods of comparing simple geometry to end-use designs are not applicable. Research limitations/implications: The mechanics of non-planar lattice structures fabricated using curved-layer additive manufacturing have not been studied thoroughly. Furthermore, traditional approaches do not apply due to parameterization deformations, requiring novel approaches to their study. Here the properties of such structures under cyclic-loading are studied experimentally for the first time. Applications for this type of structures can be found in areas like biomedical scaffolds and stents, sandwich-panel packaging, aerospace structures and architecture of lattice domes. Originality/value: This work presents an experimental approach to study the mechanical properties of non-planar lattice structures via quasi-static cyclic loading, comparing variations across several lattice patterns including auxetic sinusoids, disrupted sinusoids and their equivalent-density quadratic patterns. [ABSTRACT FROM AUTHOR]

In this paper, a pseudo-rigid body model is proposed for the analysis of a spatial mechanical metamaterial and its application is demonstrated. Using this model, the post-buckling behavior of the mechanical metamaterial can be determined without the need to consider the whole elastic structure, e.g., using finite-element procedures. This is done by analyzing a porous cylindrical mechanical metamaterial using a rigid body mechanism, consisting of rigid squares that are connected at their corners. Stiffness in this model comes from torsion springs placed at the connections between rigid parts. The theory of the model is presented and the results of two versions of this model are compared through experiments. One version describes the metamaterial in the free state, while the other, more extended, version includes clamped boundaries, matching the conditions of the experimental set-up. It is shown that the mechanical behavior of the spatial metamaterial is captured by the models and that the shape of the metamaterial in the deformed state can be obtained from the more extended model. [ABSTRACT FROM AUTHOR]

• An efficient DNN-based design framework for functionally graded lattices is established. • Functionally graded lattices are designed using the framework, fabricated using addictive manufacturing, and evaluated using experimental tests. • The effectiveness of the design framework is demonstrated with the performances of the functionally graded lattices. • This work is inspirable to promote advanced structures/materials with tailored properties. Auxetic materials with counterintuitive negative Poisson's ratio have been of significant interest due to potential applications across diverse engineering fields. Functionally grading such auxetics further enables customization of the structural response and harnesses the potential for multi-functional applications. However, a critical challenge in designing functionally graded lattices is to efficiently determine the spatial variation of the functional gradient and the corresponding geometric designs to achieve the desired response. In this paper, a highly efficient deep learning-based inverse design framework for functionally graded tetra-petal auxetics with spatially tailored properties is presented. This framework significantly improves the efficiency of tailoring functionally graded auxetics where many unit cells need to be tailor-designed. The graded tetra-petal auxetics obtained from the inverse design framework are additively manufactured and subjected to impact tests. The results show superior impact performance compared with uniform designs, demonstrating the effectiveness of the proposed inverse design framework, which can be inspirable to promote advanced structures/materials with enhanced impact resistance. [ABSTRACT FROM AUTHOR]

In this paper, the dynamic behavior of a three-layered sandwich beam with a metal foam core is investigated. Outer layers of the sandwich beam are made of AlSi12 alloy and the core is metal porous foam made of AlSi12. Numerical analysis is made for different parameters of the core -- average damping loss factor, densities, Young modulus, and Poisson's ratio of core foam. The simulations are used to determine the mechanical impedance for a sandwich beam with the applied harmonic load. Numerical calculations are made with the use of finite element method. The results imply that the auxetic core of the composite beam can have a great impact on the dynamic behavior (mobility) of the system. Furthermore, it appears that there are ranges of frequencies in which the mobility of the system can be minimized by using the auxetic foam core. [ABSTRACT FROM AUTHOR]

This work describes the identification of the shear modulus of open cell polyurethane thermoformed auxetic foams from 3- and 4-point bending tests. The foams are incorporated in sandwich beams with carbon fibre/epoxy face skins, and benchmarked against similar sandwich structures made with the conventional counterpart open cell foam. Three types of beams are tested: one with auxetic foams, another type related to a conventional foam core with the same thickness of the auxetic porous materials, and a third type of beam consisting in conventional foam with a thickness corresponding to an iso-weight configuration to the auxetic specimen. The auxetic foam has a shear modulus 7% lower than the one of the bulk conventional specimens, but higher shear stresses at large deformations and a smoother strain stiffening response compared to the beams with the conventional thinner core. The paper also highlights the low shear wave speed of these auxetic foams compared to other porous polymers used in helmet and head protection applications, as well as potential uses of the quasi-zero-stiffness behavior here observed for the auxetic foam sandwich beam. [ABSTRACT FROM AUTHOR]

The contact problem between two bodies: plate and semi-cylindrical bar is studied in this paper. The analysis concerns the contact pressure distribution along the contact region, as well as the deflection of the plate. Furthermore, the case of a composite plate covered with the auxetic layer is also considered. The influence of the Poisson's ratio of the layer on the behavior of the plate is studied. The contact pressure distribution along the contact area is analyzed using finite element analysis. [ABSTRACT FROM AUTHOR]

Helical arrangements are very common both in nature and in artificial structures. In this paper, an analysis of a prismatic composite bar is presented. The cross-sectional shape of the bar is described by a regular polygon. The composite is built of two homogeneous isotropic materials characterised by different Poisson's ratios one of which can be negative. Spatial distribution of materials in the composite is based on helical shape. Both materials are connected with the use of a transition zone of assumed width. The bar is subjected to torsional loading and its behavior is investigated by means of FEM method. Both material properties and the parameters of helical shape are investigated and the result of numerical analysis is presented. [ABSTRACT FROM AUTHOR]

This paper presents an experimental study of tensile and deformation behavior of an auxetic plied yarn structure. The basic configuration of the plied structure formed with two soft yarns and two stiff yarns was firstly introduced. Based on this 4-ply helix structure, six kinds of yarn samples were made by different combinations of soft yarns, stiff yarns and twist levels. These yarn samples were first tested and the effects of different design parameters were analyzed. Apart from the tensile test, changes in the internal structure of two samples upon stretching were also studied through microscopic examination. Finally, double helix yarn and 6-ply auxetic yarn were made for a comparative purpose to investigate the effect of helical structure. The study shows that all of the 4-ply auxetic yarn samples exhibit negative Poisson's ratio (NPR) throughout the entire tensile process, and the magnitude of NPR gets larger with a smaller soft yarn diameter, a higher tensile modulus of stiff yarn and a lower twist level. The study also shows that auxetic behavior inside the 4-ply structure is generated by the interplay between the soft yarns and stiff yarns and 4-ply auxetic yarns have the advantages to produce immediate auxetic effect upon stretching. [ABSTRACT FROM AUTHOR]

We propose in this paper analytical and numerical models that describe the in-plane uniaxial elastic properties (Young's moduli and Poisson's ratios) of a honeycomb structure with curved walls. We perform a parametric analysis of the mechanical performance of this honeycomb also by taking into account the different types of deformations acting inside the cell walls. The curved wall honeycomb possesses higher magnitudes of the Poisson's ratio ν12 in the auxetic configuration compared to classical center symmetric configuration with straight cell wall. The presence of the curvature also allows creating configurations with positive Poisson's ratio even for negative internal cell angles, and makes this honeycomb design attractive for mechanical tailoring. [ABSTRACT FROM AUTHOR]

[Display omitted] • Deflection behaviour of existing auxetic re-entrant beams compared with traditional beam designs. • Overlooked factors of placement and orientation of auxetic clusters utilized for enhancement. • Two new improved auxetic beam designs proposed with minimal deflection and 64% reduction in material. • Usefulness of the proposed designs brought out by application into lightweight foot bridge design. Auxetic materials have gained popularity in engineering applications owing to their unique deformation response mechanism. However, they have not been exploited to their full potential in engineering load bearing applications. The current paper, therefore, is focused on exploring and improving the deflection behaviour of auxetic beam structures. Initially, a single re-entrant unit cell and an array of auxetic clusters are modelled using Finite Element Method (FEM). These numerical models are then verified for its Poisson's ratio and deflection behaviour using theoretical formulations. Subsequently, in the next phase, a comparison of the deflection characteristics of the in-use common beams with that of the conventional auxetic beam design is carried out. Much overlooked factors such as orientation and placements of auxetic clusters are introduced in beam designs and are exploited to improve the deflection characteristics of conventional auxetic beams. Through this assessment, the paper proposes two novel design concepts of Oriented Re-entrant Structures (ORS) and Assorted Re-entrant Structures (ARS) for improved load bearing response. Novel designs of ORS and ARS beams are observed to perform significantly better than the conventional auxetic and honeycomb beams. The newly proposed beam designs exhibit a 64% reduction in mass in comparison to the homogeneous beam. The usefulness of these designs are brought out by introducing the ARS auxetic beams into a real-world lightweight foot bridge design. The bridge designs with ARS cross beams demonstrates a better behaviour in comparison to the bridge designs with conventional cross beams in terms of both deformation and material usage. This work highlights the potential use of unconventional mechanical metamaterial structures in engineering load bearing problems to address the demands of green engineering and sustainability without compromising on its structural integrity. [ABSTRACT FROM AUTHOR]

In this paper, we introduce methods of constructing structures with rigid sliding units that exhibit auxetic behavior, namely, have negative Poisson's ratio. First, we illustrate how we can construct 2-dimensional (2D) auxetic structures with bow-tie shaped rigid sliding hexagonal units. Next, we show that we can construct 3-dimensional (3D) auxetic structures by arranging hourglass shaped rigid sliding units in regular triangular configuration or in regular square configuration. Also, we show, through theoretical and numerical analysis, that these structures indeed exhibit auxetic behaviors. [ABSTRACT FROM AUTHOR]

This paper reviews 2D auxetic models, including 3D deformation models with 2D auxetic behavior, from mechanism perspective instead of geometrical perspective. On this basis, auxetic models across different geometrical groups can be regrouped into clusters that exhibit analogy in deformation mechanism. Factors that are taken into consideration include the identification of corresponding (i) rotation and non-rotation units, as well as (ii) linkages/joints between rotation and non-rotation units and non-linkages/non-joints across various auxetic models. As a result, five clusters of auxetic models have been identified, in which auxetic models within each cluster are analogous to each other. The identified clusters are those that exhibit: (a) double periodicity in the rotation direction of their rotating units, (b) synchronized rotation direction of their rotation units, (c) single periodicity in the rotation direction of their rotating units, (d) random rotation of their rotation units, and (e) non-rotation of units. Results from this analogy identification place auxetic models in a systematic representation and will enrich future development of auxetic models, particularly those that do not fall within these five clusters. It is proposed that future work includes 3D auxetic models as well as ordering of analogous auxetic models according to their joints or linkage geometries. [ABSTRACT FROM AUTHOR]

In this paper, the bending performances of sandwich panels with corrugated triangular, honeycomb, aluminum foam, pyramidal truss, double sine corrugated (DSC), and 3D re-entrant auxetic cores are assessed and compared, both experimentally and numerically. Three-point bending experiments were performed on corrugated, honeycomb, aluminum foam, and truss core sandwich panels with identical face-sheets and core height. The experimental and numerical results compared well for panels with corrugated, honeycomb and truss cores. Parametric studies were subsequently performed, using ABAQUS, and three distinct modes of deformation were identified. The specific energy absorption (SEA) of the panels was found to increase with the core relative density; the one with a honeycomb core will be shown to have the greatest SEA, for the same core relative density, compared to the rests. • Corrugated, honeycomb, foam, and truss sandwich panels were experimentally tested. • Parametric studies were conducted on panels with various types of cores. • The deformation and specific energy absorption of sandwich panels were compared. [ABSTRACT FROM AUTHOR]

The torsion of a prismatic beam has been a classic problem of structural mechanics since the famous works of Saint-Venant. In this paper, an analysis is extended on a composite beam with elliptical cross-section. We consider a beam in which the elliptical cross-sectionis split into sectors inwhichtwo materials, one of which is auxetic, are distributed alternately. The influence of auxetic phase on the total elastic strain energy is analyzed as well as geometrical parameters representing both the shape of the cross-section, and the arrangements of sectors. An unexpected behavior of a beam with strong auxetic phase is presented as, in the case of selected parameters, the beam with elliptical crosssection is more rigid than the beam with a circular one. [ABSTRACT FROM AUTHOR]

Auxetic materials are endowed with a behavior that contradicts common sense, when subjected to an axial tensile load they increase their transverse dimension. In case of a compression load, they reduce their transverse dimension. Consequently, these materials have a negative Poisson's ratio in such direction. This paper reviews research related to these materials. It presents the theories that explain their deformation behavior and reveals the important role represented by the internal structure. Their mechanical properties are explored and some potential applications for these materials are shown. [ABSTRACT FROM AUTHOR]

The paper deals with the extended thermodynamical model of thermoelastic interactions in nonlinear elastic solids of anomalous mechanical properties (negative Poisson's ratio materials) including energy dissipation during the thermoelastic damping phenomenon. The model has been based, among others, on Murnaghan's free energy. Numerical simulations show unconventional effects occurring in such materials. [ABSTRACT FROM AUTHOR]

• Introducing dual-material auxetic meta-sandwiches by 4D printing technology. • Arranging soft hyper-elastic polymers and elasto-plastic hard shape memory polymers. • Proposing reversible energy absorbers by leveraging instability and elasto-plasticity. • Implementing finite element methods to predict experimental observations. • Showing high capability of reversible meta-sandwiches for dissipating energy. The aim of this paper is to introduce dual-material auxetic meta-sandwiches by four-dimensional (4D) printing technology for reversible energy absorption applications. The meta-sandwiches are developed based on an understanding of hyper-elastic feature of soft polymers and elasto-plastic behaviors of shape memory polymers and cold programming derived from theory and experiments. Dual-material lattice-based meta-structures with different combinations of soft and hard components are fabricated by 4D printing fused deposition modelling technology. The feasibility and performance of reversible dual-material meta-structures are assessed experimentally and numerically. Computational models for the meta-structures are developed and verified by the experiments. Research trials show that the dual-material auxetic designs are capable of generating a range of non-linear stiffness as per the requirement of energy absorbing applications. It is found that the meta-structures with hyper-elastic and/or elasto-plastic features dissipate energy and exhibit mechanical hysteresis characterized by non-coincident compressive loading-unloading curves. Mechanical hysteresis can be achieved by leveraging elasto-plasticity and snap-through-like mechanical instability through compression. Experiments also reveal that the mechanically induced plastic deformation and dissipation processes are fully reversible by simply heating. The material-structural model, concepts and results provided in this paper are expected to be instrumental towards 4D printing tunable meta-sandwiches for reversible energy absorption applications. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Rational design of artificial micro-structured metamaterials with advanced mechanical and physical properties that are not accessible in nature materials is challenging and important. In our paper, mechanical designs of 2D and 3D chiral mechanical metamaterials are reviewed, and their mechanical behaviors and deformation mechanisms can be investigated through equilibrium principle, strain energy analysis, micropolar elasticity and homogenization theories. Afterwards, multifunctional properties of chiral mechanical metamaterials are elaborated, such as: vibration attenuation, impact energy absorption and negative coefficient of thermal expansion (CTE). Finally, several successful industrial applications of chiral mechanical metamaterials are demonstrated, such as: morphing airfoil smart deployable antenna and reconfigurable structures, auxetic stent, chiral flexible electronics and phase transforming metastructures, etc. Finally, perspectives and challenges on chiral mechanical metamaterials are discussed. Rational design of artificial micro-structured metamaterials with advanced mechanical and physical properties that are not accessible in nature materials is challenging and important. In the past several years, making use of the node rotation and ligament bending deformation features of chiral elements, various types of 2D and 3D chiral mechanical metamaterials are designed and proposed for industrial application. In our paper, mechanical designs of 2D and 3D chiral mechanical metamaterials are reviewed, and their mechanical behaviors and deformation mechanisms can be investigated through force and momentum equilibrium principle, strain energy analysis, micropolar elasticity and homogenization theories. Afterwards, multifunctional properties of chiral mechanical metamaterials are elaborated, such as: vibration attenuation and bandgap features, impact energy absorption and negative coefficient of thermal expansion (CTE). Finally, several successful industrial applications of chiral mechanical metamaterials are demonstrated, such as: morphing airfoil with chiral core configuration, shape memorial smart deployable antenna and reconfigurable structures, auxetic stent for biomedical application, chiral flexible electronics and phase transforming metastructures with shape switching abilities, etc. Unlabelled Image • Design of chiral mechanical metamaterials are reviewed, theoretical models are elaborated for exploring the deformation mechanisms. • Multifunctional mechanical benefits and limitations of chiral mechanical metamaterials are reviewed and discussed. • Industrial applications of chiral mechanical metamaterials are reviewed, perspectives and challenges are discussed. [ABSTRACT FROM AUTHOR]

• Effectiveness of re-entrant auxetic structure under close-in and far-field blasts. • Evaluation of protective efficacy of auxetic honeycomb-core sandwich panel. • Performance comparison with equivalent conventional honeycomb. This paper aims to scrutinise the effectiveness of a re-entrant auxetic honeycomb-core sandwich panel (AHSP) to protect reinforced concrete (RC) slab under close-in and far-field detonations of high explosive. A series of quarter symmetric 3D comprehensive numerical models were developed by using Arbitrary Lagrangian Eulerian (ALE) formulation in LS-DYNA hydrocode. Strain rate effects of the rate sensitive materials were employed in the model to consider dynamic behaviour of the materials during blast loading. The developed numerical model was validated with the documented experimental results. Deformation patterns, energy absorption, overpressure damping, blast pressure deflection, and stress-transmission to the protected structure were investigated with the computational models. Furthermore, the performance of AHSP sacrificial protective structure was compared with an equivalent areal density conventional honeycomb-core sandwich panel (CHSP) structure. The results showed that AHSP not only absorbed higher blast energy but also acted as a pressure deflector by forming a densified concave depression under close-in blast load. AHSP damped higher magnitude of blast overpressure in both close-in and far-field blasts. Moreover, a uniform redistribution of the stress on the protected structure was observed with AHSP protection. The overall response of AHSP was found to be better than CHSP to protect the RC slab. [ABSTRACT FROM AUTHOR]

A new method for the production of thin flat and curved auxetic foam sheets by uniaxial compression is reportted in this paper. Detailed optical microscopy and Poisson's ratio measurement by videoextensometry has revealed that the auxetic behaviour is due to a crumpling of the pores through the foam thickness, caused by a uniaxial compression of 40-60% in combination with shear for the curved foams. Poisson's ratio values of up to −3 have been recorded for the curved foams and −0.3 for the flat sheets. [ABSTRACT FROM AUTHOR]

Materials with unusual mechanical properties can be potentially used as matrices to create high-performance lightweight composites. The appearance of materials with negative Poisson's ratio (auxetics), has led to the evaluation of auxetic composites for possible engineering applications. Because the experimental evaluation of composites with specific properties is expensive and time consuming, computational modelling and simulation provide efficient alternatives to predict the parameters of the composites. In this paper a finite element method was used to find the engineering constants (Young's modulus and Poisson's ratio) of auxetic composites consisting of concentric cylindrical inclusions made of combinations of auxetic and classic (non-auxetic) materials. It has been observed that not only the mechanical properties of the different composite phases influence the effective mechanical properties of the whole composite, but also the location of the same material phases do matter. [ABSTRACT FROM AUTHOR]

• Novel auxetic topology computation with an objective of energy absorption maximisation for the first time. • Derivation of analytical design parameters of the novel auxetic structures with consideration of fabrication practicality. • Examination of mechanical properties and energy absorption of the developed auxetic structures to evaluate protective performance based on peak elastic stress, plateau stress, onset of the densification strain and energy absorption capability. This paper aims to develop lightweight high-performance auxetic structures for protective applications such as blast and impact energy absorption. In this study, novel auxetic topologies were computed with an objective of energy absorption maximisation through the topology optimisation method. Analytical design formulations with the consideration of fabrication practicality were derived for the novel auxetic structures; named as the hourglass structure (HGS), braced cross-petal structure (BCPS) and cross-petal structure (CPS). Based on the formulated design parameters, rectangular scaffolds of each structure were designed to investigate bulk mechanical properties and energy absorption under a compressive load. Validated nonlinear finite element (FE) models developed in LS-DYNA FE code were used to examine the mechanical performance of the novel structures. The FE simulations revealed the deformation mechanism, negative Poisson's ratio, stress-strain behaviour and energy absorption. The protective performances of the developed auxetic structure were evaluated with respect to the peak elastic stress, plateau stress, onset of the densification strain and energy absorption capacity. The HGS outperformed the other structures in term of the protective performance. In addition, comparison of specific energy absorption at the onset of densification showed that the HGS, BCPS and CPS possessed superior energy absorption capacities than the conventional auxetic structures. [Display omitted] [ABSTRACT FROM AUTHOR]

The elastic properties of f.c.c. hard sphere crystals with periodic arrays of nanoinclusions filled by hard spheres of another diameter are the subject of this paper. It has been shown that a simple modification of the model structure is sufficient to cause very significant changes in its elastic properties. The use of inclusions in the form of joined (mutually orthogonal) layers and channels showed that the resulting tetragonal system exhibited a complete lack of auxetic properties when the inclusion spheres reached sufficiently large diameter. Moreover, it was very surprising that this hybrid inclusion, which can completely eliminate auxeticity, was composed of components that, alone, in these conditions, enhanced the auxeticity either slightly (layer) or strongly (channel). The study was performed with computer simulations using the Monte Carlo method in the isothermal-isobaric ( N p T ) ensemble with a variable box shape. [ABSTRACT FROM AUTHOR]

• 4D printed programmable shape memory polymer-based auxetics are investigated. • The shape memory polymer displays the temperature memory effect. • A negative 'Poisson's ratio equal to about −0.18 is found. • Sequential in-plane and out-of-plane motions of auxetics can be easily programmed. • Results are general and can be applied to any auxetic geometry. 4D printing refers to a novel trend in the field of active materials, regarding the employment of additive manufacturing to obtain structures presenting inherent complex shapes and shape evolutions under the application of proper stimuli. Such a technique is a powerful tool to realize auxetic structures with customized architectures and programmable/controllable shape change. The present paper proposes 4D printed shape memory polymer-based systems with auxetic structure, capable of hierarchical motion. The systems were prepared starting from a commercial photopolymer by means of stereolithography. The mechanical behavior of the systems was characterized in uniaxial tensile tests, measuring the strains parallel/perpendicular to the load direction. Thanks to a broad glass transition region, the photopolymer displays the so-called "Temperature-Memory Effect" (TME), i.e. the possibility to tailor the thermal trigger of the Shape-Memory Effect (SME) through the deformation temperature. Thermo-mechanical histories were applied to a single unit cell to investigate both the overall shape memory response and the possibility to undergo multiple combined out-of-plane and in-plane motions on the basis of the TME. Obtained results allow discussing the effect of deformation temperatures on the thermal region triggering the SME and show the possibility to exploit the TME to achieve sequential self-deployment of auxetic structures. [ABSTRACT FROM AUTHOR]

This paper introduces a class of honeycomb composite metamaterials whereby the increase and decrease in temperature give rise to opposing microstructural geometries in situ , thereby leading to Poisson's ratio of opposing signs. The metamaterial consists of rigid crossbeams from which alternating bimaterials are joined onto. Four types of this class of metamaterial, depending on the relative location of the bimaterial phase with higher coefficient of thermal expansion within each unit cell, have been identified. The O-Type and X-Type metamaterials, in which each unit cell has 2 axes of symmetry, exhibit sign-reversal of Poisson's ratio upon temperature change sign reversal. The CC-Type has one axis of symmetry in each unit cell while the SS-Type possesses a 180-degree rotational symmetry; these metamaterial types display zero Poisson's ratio and zero thermal expansion in a specific direction. This class of metamaterial avails to the practising engineer the possibility of designing materials and structures with in situ sign-switchable Poisson's ratio by means of thermal-toggling, as well as those that require good dimensional stability. [ABSTRACT FROM AUTHOR]

Auxetics with negative Poisson's ratio (NPR) can expand dimensions along the direction perpendicular to the tensile direction, such as rigid rotation, reentrant and chiral structures, etc. The mechanical performances of chiral metastructures are closely related to internal defects and interactions between defects. In this paper, two types of irregular chiral structures with Gaussian dispersion of circular node positions and missing ligaments are designed, namely: anti‐tetrachiral metastructure and tetrachiral hybrid metastructure. These two types of chiral metastructures are characterized by node radius, ligament thickness, ligament length, the circular node center dispersion range, and missing ligament percentages. Effects of random node distribution range and cell wall missing percentage on the elastic modulus and Poisson's ratio of chiral metastructures are investigated through experimental tests and finite element (FE) simulation systematically. Through dimensionless analysis, it is found that ligament thickness has remarkable influence on the negative Poisson's ratio. Effect of missing ligament on the mechanical properties of the structure is greater than effect of random node center dispersion. With the increase of ligament missing percentage, the resultant modulus of chiral metastructures decreases, and the corresponding NPR increases. [ABSTRACT FROM AUTHOR]

Three 3D models with negative compressibility have been presented in our previous paper [X. Q. Zhou et al., Phys. Status Solidi B 2016, 253, 1977]. However, the 2D mechanism (i.e., wine‐rack mechanism) which we used to design 3D models is so symmetrical that the axial properties of it are equivalent, so we have only focused on geometry features. In this work, an extended study is conducted in order to find a more efficient method to design 3D structures with evident negative compressibility. Through theoretical modeling, the compressibility properties of three 3D models made from hinging hexagonal truss mechanism are analyzed and the conditions for negative compressibility to be exhibited are discussed. The study shows that in addition to the geometry features, negative compressibility effects can also be significantly affected by the arrangement of the framework and layout orientations of 2D mechanism. The compressibility properties of three 3D models made from hinging hexagonal truss mechanism are analyzed and the conditions for the negative compressibility to be exhibited are discussed. It is shown that in addition to the geometry features which have already been widely discussed, the arrangement of the framework and the layout orientations of 2D mechanisms can also have a great influence on the negative compressibility effect. [ABSTRACT FROM AUTHOR]