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A theoretical model has been developed to express the longitudinal and transverse piezoelectric effects in ferro/piezoelectrets. This model is an extension of the classic model based on layer-dielectric structures that focuses on the longitudinal piezoelectric effect. The improved model reveals that the relation between the longitudinal piezoelectric d33 coefficient and the transverse piezoelectric d31 coefficient is associated with Poisson's ratio μ13 (or μ31) and Young's moduli Y1 and Y3. The polarity of the two coefficients is opposite for materials with a positive Poisson's ratio as normally observed in conventional piezoelectric materials, and the same for materials with a negative Poisson's ratio, i.e., auxetic materials. The experimental results available in the literature and obtained from ferroelectret metamaterials with a honeycomb cross-sectional structure and two-dimensional (2D) symmetric structure, called 2D ferroelectret metamaterials, designed and prepared in this study reasonably agree with theoretical predictions. This study not only extends the scope of the metamaterials by inducing the concept of ferroelectret metamaterials but also provides a strategy for designing ferroelectrets with designable properties. [ABSTRACT FROM AUTHOR]

This paper presents a novel rhombic star-shaped honeycomb (RSSH) configuration with tunable Poisson's ratio and elastic modulus, and an RSSH with the U-shaped ligaments (URSSH) configuration is generated to analyze the effect of the curved ligaments on the elastic properties of RSSH. Cellular structure of RSSH combines with a rhombic and an improved star-shaped geometry, which can also be subdivided into flexible segments and rigid segments. In-plane elastic properties of the RSSH cell, including Poisson's ratio and elastic modulus, are both derived by analytical model based on flexibility modeling method and Castigliano's second theorem. Based on the guidance of theoretical model, quasi-static tensile experiments and finite element simulation of RSSH and URSSH specimens are carried out with different Poisson's ratio. The experimental results are in good agreement with the theoretical predictions and finite element analysis results. Length of cellular ligaments Lt1, dt have linear relationship with mechanical properties of the RSSH cell under constant angle θ1 and make the cellular configurations with different Poisson's ratio more obtainable. The effect of the symmetry of the flexible segments on the cellular mechanical properties is also analyzed through theoretical prediction. The introduction of asymmetry can bring wider design space of RSSH mechanical properties, especially Poisson's ratio. This work demonstrates the promising potential for applying RSSH configurations in 2D morphing structures with tunable auxetic behaviors. [ABSTRACT FROM AUTHOR]

In this article, the non‐linear free vibration behavior of sandwich composite panels with sinusoidal corrugations is examined. These panels consist of a top and bottom skin made of a graphene‐reinforced composite, with an auxetic honeycomb core having negative Poisson's ratio. The non‐linear kinematic field is based on Kant's higher‐order shear‐deformation theory and the Green‐strain, which incorporates all the higher‐order terms. By implementing the Hamilton principle, the non‐linear governing equations are affirmed and solved further through 2D‐isoparametric finite element approximations via Lagrangian elements in conjunction with Picard's successive iterative scheme. The comparison and validation tests demonstrate the correctness of the present model. The established sandwich model is further employed for various parametric conditions by varying the core‐to‐face sheet thickness, auxetic honeycomb properties, graphene volume fraction, shell configurations, temperature, and support conditions. These numerous results exemplify the non‐linear frequencies at small‐to‐large amplitudes for the sandwich shell structures and are discussed in detail. In addition, a multi‐objective parametric optimization is conducted using the response surface method to investigate the optimal values of the corrugated auxetic honeycomb shell panel's parameters, resulting maximum frequency. Highlights: Non‐linear vibration of corrugated sandwich shell panel.Graphene reinforced skins and honeycomb auxetic core.Kant's higher‐order shear‐deformation theory and Green‐Lagrange non‐linearity.Hamilton principle and Picard's successive iterative scheme.Multi‐objective parametric optimization and prediction using response surface methodology. [ABSTRACT FROM AUTHOR]

Lattice structures nowadays have gained a peak in research. Inspired by the honeycomb structure and fishbone, this study investigated lattice structures that can provide auxetic behavior and store maximum energy absorption during deformation mode. From that, the study involved designing and producing different modified lattices based on the honeycomb's structure and the fishbone's perspective. The specimens were 3D printed within fused filament fabrication techniques within the additive manufacturing platform of Euromed University of Fes. The conception, production, mechanical testing, and simulation have been employed to get optimum data analysis of the mechanical properties of the designed structures. The results observed under quasi-dynamic compression did not show significant densification behavior; but, the auxetic behavior was seen in all structures, while some suddenly collapsed. The experimental and numerical analysis demonstrated similar deformation behavior and strong agreement in their respective results. Nevertheless, some discrepancies in mechanical values were observed, with a relative percentage error of approximately 1% for both methods. Consequently, owing to the enhanced energy absorption observed in the V2 and V3 structures, it is evident that these modifications hold promise for optimizing the performance of these metamaterials in various practical applications. [ABSTRACT FROM AUTHOR]

• Impact response of stiffened sandwich FGPM doubly-curved shell with re-entrant honeycomb auxetic core is studied. • The interaction between the impactor and shell utilizes equivalent spring-mass (SM) model consisting two-degrees-of freedom. • The facesheets are made from FGPM and the shell structure is modeled by first order shear deformation theory. • The impact performance of re-entrant honeycomb auxetic core is compared with regular hexagonal honeycomb core. Owing to unique deformation behavior and high capacity of energy absorption, auxetic structures have garnered significant research attention. To reveal the energy-absorbing properties of the auxetic structure, the impact response of stiffened sandwich functionally graded porous materials (FGPM) doubly-curved shell with re-entrant honeycomb auxetic core is studied by the established analytical model in the present work. The material properties in the thickness direction of FGPM face sheets are adjusted according to the volume fraction of constituents by power law and exponential law, while the core layer is made of the re-entrant honeycomb auxetic core with negative Poisson's ratio. On the basis of the Hertz theory for elastic impacts and the first-order shear deformation theory (FSDT), an analytical model is developed to study its impact phenomenon. Equations of motion are derived using Hamilton's principle, which are further solved analytically using Navier's technique of assuming unknown variables in the double trigonometric series. The time-dependent contact force is obtained by applying the spring-mass (SM) model consisting two-degrees-of freedom. Afterward, the transverse central displacements of the stiffened sandwich FGPM doubly-curved shell are calculated by adopting the Duhamel integration. The impact force and transverse displacements are compared with the previously published results, indicating that the theoretical results agree with the previously published results. Parametric analyses have been carried out to investigate the effect of variation of various parameters such as volume fraction exponents, radii of principal curvatures, porosity volume fraction, core layer inclined angle on the impact response of the sandwich shell. Additionally, the results show that compared with the traditional hexagonal honeycomb core type, the stiffened sandwich FGPM doubly-curved shell with re-entrant honeycomb core type has significant advantages in impact energy absorption. This work may provide an extensive reference and valuable guidance in the impact design and application of auxetic sandwich shell structures. [ABSTRACT FROM AUTHOR]

This study aims to improve the impact protection performance of composite structures by combining a honeycomb core with negative Poisson's ratio and graphene platelets reinforced (GPR) face sheets. The paper investigates the nonlinear repeated low-velocity impact responses of auxetic honeycomb composite plates, taking into account loading-unloading-reloading processes. Effective material properties of the auxetic honeycomb core and GPR face sheets are obtained by using the proposed modified Gibson function and Halpin-Tsai model. Then, taking into account geometric nonlinearity, the nonlinear equations of motion for the system were derived by Hamilton's principle. Afterward, the time-varying contact force between the composite plate and a spherical impactor is defined by the modified nonlinear Hertz contact theory. The Galerkin method and variable-step Runge-Kutta algorithm are selected to obtain nonlinear impact responses. The proposed methods are verified by finite element simulation and experiment. Finally, the study evaluates the effects of key parameters on the nonlinear repeated low-velocity impact responses. [ABSTRACT FROM AUTHOR]

Purpose: Fused filament fabrication (FFF) is a popular technique in rapid prototyping capable of building complex structures with high porosity such as cellular solids. The study of cellular solids is relevant by virtue of their enormous potential to exhibit non-traditional deformation mechanisms. The purpose of this study is to exploit the benefits of the FFF technology to fabricate re-entrant honeycomb structures using thermoplastic polyurethane (TPU) to characterize their mechanical response when subjected to cyclic compressive loadings. Design/methodology/approach: Specimens with different volume fraction were designed, three-dimensionally printed and tested in uniaxial cyclic compressions up until densification strain. The deformation mechanism and apparent elastic moduli variation throughout five loading/unloading cycles in two different loading orientations were studied experimentally. Findings: Experimental results demonstrated a nonlinear relationship between volume fraction and apparent elastic modulus. The amount of energy absorbed per loading cycle was computed, exhibiting reductions in energy absorbed of 12%–19% in original orientation and 15%–24% when the unit cells were rotated 90°. A softening phenomenon in the specimens was identified after the first compression when compared to second compression, with reduction in apparent elastic modulus of 23.87% and 28.70% for selected samples V3 and H3, respectively. Global buckling in half of the samples was observed, so further work must include redesign in the size of the samples. Originality: The results of this study served to understand the mechanical response of TPU re-entrant honeycombs and their energy absorption ability when compressed in two orientations. This study helps to determine the feasibility of using FFF as manufacturing method and TPU to construct resilient structures that can be integrated into engineering applications as crash energy absorbers. Based on the results, authors suggest structure's design optimization to reduce weight, higher number of loading cycles (n > 100) and crushing velocities (v > 1 m/s) in compression testing to study the dynamic mechanical response of the re-entrant honeycomb structures and their ability to withstand multiple compressions. [ABSTRACT FROM AUTHOR]

This study proposes to investigate the crushing performance of auxetic honeycombs by combining liquid and solid phase materials in one structure. The multiphase structures were produced by injecting a liquid Gallium metal into the hierarchical voids of the proposed metamaterials and tested at different temperatures (22 and 35 0C), where the melting temperature of Gallium metal is 29.4 0C. The deformation mechanism, compressive strength, absorbed energy, and Poisson's ratio (PR) of the samples was compared at different strains and at different temperatures. Results show that multi-material samples with Gallium metal lead to a progressive deformation mechanism and stabilize the fracture mechanism; however, they only exhibit larger compressive strength in a few cases. In addition, the effects of the phase change of Gallium from solid to liquid when the temperature increase from 22 0C to 35 0C stand out in the percent change of mechanical response. Overall, the presented samples in this work can be recommended to manipulate the collapse mechanism with a multi-material approach of liquid and solid constituents. [ABSTRACT FROM AUTHOR]

Auxetic metamaterials with two components exhibit a wide variety of potential engineering applications due to their exotic mechanical properties. In this work, a novel straight-arc coupled structure (SACS) is designed by introducing a circular arc structure to a classical re-entrant structure. This work aims to explore the linear and geometrical nonlinear mechanical of SACS at large strains. According to Castigliano's second theorem, the in-plane linear theoretical model is established to obtain equivalent Poisson's ratio and elastic modulus. A geometrical nonlinear model is further established based on large deflection theory and chain algorithm. The finite element method is used to verify the prediction of the theoretical solution, and linear and nonlinear mechanical properties of the SACS are studied by numerical simulation. The influence of geometric parameter re-entrant angle and arc radius on the mechanical properties of the SACS is investigated to compare the linear and nonlinear mechanical properties. The linear numerical simulation of SACS with two transverse ribs (SACS-TR) and classical re-entrant honeycomb structure with two transverse ribs (CRS-TR) is carried out to analyze the in-plane elastic properties. These results demonstrate that considering the geometric nonlinear model can predict the actual structural deformation more accurately, which is verified by the quasi-static compression experiment results at large strains. The SACS design can enhance the auxetic effect and structure Young's moduli under the same dimension. [ABSTRACT FROM AUTHOR]

Auxetic honeycomb has unique mechanical properties such as good energy absorption capacity, tensile strength and fracture toughness, etc. Therefore, honeycomb with a negative Poisson's ratio is used widely in medical, biological, aerospace and other fields. This honeycomb has large deformations in energy absorption and vibration reduction. It is very important to study the nonlinear constitutive of the honeycomb structure. Therefore, this paper establishes the nonlinear constitutive relationship of the auxetic honeycomb structure under large deformations. This constitutive relation includes the in-plane stress, in-plane strain, Young's modulus and Poisson's ratio of the negative Poisson's ratio honeycomb. The finite element model of the negative Poisson's ratio honeycomb cells is established, and the calculated results of finite element model are compared with that of the theoretical calculation results. On this basis, the influence of the geometric parameters on the mechanical properties of the structure is studied. The results of this paper will provide a theoretical basis for the further study of the auxetic honeycomb sandwich structure and provide a basis for the engineering application of honeycomb structures. [ABSTRACT FROM AUTHOR]

In this paper, the energy absorption capacity of continuous fiber-reinforced thermoplastic auxetic structures is examined experimentally and the results compared with both numerical and analytical methods. To this extent, a 3 D printing technology of Fused Deposition Modeling (FDM) is implemented for fabricating the auxetic honeycombs and quasi-static compression test is conducted to extract the load-displacement behavior of the structure. Both hollow and foam filled lattice structures are tested, and the results revealed that the absorbed energy increased by 20% for PLA and 70% for PA specimens, when using foam. Finite element analysis is also performed using the explicit solver. The onset of failure is determined using the maximum stress criterion and VUSDFLD subroutine and the damage growth is modeled by decreasing the mechanical properties of the elements. The obtained results are in relatively good agreement with the experimental analysis. In addition, a theoretical formulation is developed and the probabilistic analysis is performed to draw the honeycomb failure design envelope, which is a practical tool for designing of various honeycomb configurations. The failure envelope shows that decreasing the strut angle increases the honeycomb failure load, however, the auxetic property of the structure decreases. [ABSTRACT FROM AUTHOR]

Auxetic metamaterials possess superior properties and have drawn extensive attention in the past decades. Herein, two curved ribs are added to the conventional re‐entrant (CRE) honeycomb structure to form a modified auxetic re‐entrant (MRE) honeycomb structure for improving the energy absorption capacity of the structure. In‐plane quasi‐static compression response of the honeycomb in large deformation is numerically explored first. Then, quasi‐static compression test is conducted to verify the validity of the numerical simulation. Both experimental and numerical simulation results reveal that during the quasi‐static compression process, two plateau stresses occur in the load–displacement curves of the structure, and the second plateau stress is much higher than the first one. The occurrence time of the second plateau stress can be controlled by the distance between the concave curved ribs in the structure. The experimental results are in good agreement with the finite element analysis results. Due to their desirable mechanical properties, the MRE honeycomb structures have great potential for applications in civil engineering, vehicle crashworthiness, and protective infrastructure. [ABSTRACT FROM AUTHOR]

2D woven auxetic fabrics (AF) developed by weave design modification provide a continuous, commercial, and low-cost manufacturing process for high strength and stable auxetic structures. However, AFs developed by previous methods have a highly folded surface, which is problematic in printing, laminating, and stitching. For the first time, we studied the auxeticity in a few yarn-based auxetic structures, which provides a uniform surface texture. Reentrant honey-comb geometry was chosen to fabricate auxetic woven fabrics, as such geometry shows the best auxetic nature. Different parameters of auxetic geometry were optimized based on their mechanical response using the statistical tool: gray relational analysis (GRA). The mechanical properties of AFs were compared with conventional (3/1 twill woven) non-auxetic fabric (NAF), having the same specifications. The smaller unit cell (3E) with a reorientation area of 4P showed optimum auxeticity and mechanical properties. The optimized auxetic structure showed superior mechanical properties as compared to conventional fabric. GRA grade of optimized AF was 67.3% higher than the NAF. Most importantly, the tensile strength was 23% higher for optimized AF structure. The bidimensional energy dissipation ability of the AF provides a key advantage in the superior mechanical response. [ABSTRACT FROM AUTHOR]

A time-dependent understanding of swelling characteristics and external stimuli behavior is crucial for the development and understanding of functional hydrogels. Magnetic resonance imaging (MRI) offers the opportunity to study three-dimensional (3D) soft materials nondestructively. This technique is already widely used as an image-based medical diagnostic tool and is applied here to evaluate complex structures of a hydrogel—a double network of chemically crosslinked casein enhanced with alginate—fabricated by 3D printing. When hydrogel disks immersed in four different liquid systems were analyzed, the material exhibited distinct system-dependent behavior characterized by rheological and mechanical measurements. Further material functionalization was achieved by macroscopic structuring of the hydrogel as an auxetic material based on a re-entrant honeycomb structure. MRI offers the advantage of monitoring overall changes in the area of the analyzed specimen and internal structural changes simultaneously. To assess the behavior of this complex structure, a series of short MRI measurements, each lasting 1.7 min, captured liquid diffusion and thus structural swelling behavior. A clear dependence of external and internal structural changes as a function of liquid properties causing these changes was observed. In conclusion, this approach might pave the way for prospective applications to monitor liquid diffusion into (e.g., vascularization) and swelling behavior of functional hydrogels. [ABSTRACT FROM AUTHOR]

The static stability of auxetic truncated conical sandwich shells reinforced by stiffeners surrounded by elastic foundations is investigated. The shells are made from two isotropic outer layers and an auxetic core layer with a negative Poisson ratio. Based on the classical shell theory, combined with the displacement and Bubnov–Galerkin methods, the governing equations of the shells are derived and solved. The critical buckling load of the shells as a function of their geometrical parameters, the honeycomb structure, stiffeners, and types of elastic foundations are examined in detail. [ABSTRACT FROM AUTHOR]

This paper examines the impact of polyurethane foam (PUF) filling on the dynamic response of honeycomb sandwich beams (HSBs) through the blast testing. The HSBs are composed of steel face sheets and an aluminium alloy honeycomb core filled with PUF. A comparative analysis of damage modes is conducted between conventional hexagonal and auxetic HSBs, considering both foam-filled and unfilled configurations. The results reveal that the HSBs with foam filling demonstrate significantly enhanced blast performance compared to their counterparts without foam filling. This superiority is evident in both global deformation and local damage characteristics. Furthermore, a well-validated numerical model is developed to examine the damage mechanisms of PUF-filled HSBs under blast loading. The investigation reveals that appropriate PUF filling methods can effectively enhance bending resistance while minimizing the decline in the energy absorption efficiency. Finally, a multiobjective optimization was conducted using the back-propagation (BP) neural network and the SPEA2 algorithm to identify the optimal position for PUF. By utilizing a reduced foam filling approach as opposed to completely filling the structure, the two optimized configurations show a decrease in deformation of 5.38 % with an equivalent specific energy absorption (SEA) or an increase in the SEA by 5.26 % with an equivalent deformation. [ABSTRACT FROM AUTHOR]

• A class of modified hexagonal honeycomb to realize pattern transformation. • Honeycomb's elastic constants are derived by theoretical energy analysis. • Honeycomb structures exhibit auxetic behavior after pattern transformation. • The cell/node of the honeycomb has a rotating behavior after pattern transformation. • The underlying mechanism of pattern transformation is revealed for honeycomb. Pattern transformation, as one of the special properties of mechanical metamaterials, is widely found in elastic porous structures and gradually expanding to honeycomb structures. Inspired by the higher-order flower-like buckling pattern of hexagonal honeycomb, and generalizing the geometry of structures that pattern transformation occurs under uniaxial compression, this paper proposes a Modified Hexagonal Honeycomb(MHH) structure by adjusting the thickness ratio α and the deflection extension angle θ of the cell wall to topologically reconstruct the honeycomb structure to initiate the first-order quasi-flower-like buckling pattern under uniaxial loading. Results show that the quasi-flower-like pattern transformation appears directly for the MHH structure under uniaxial compression, accompanied with a transition of the Poisson's ratio, from positive to negative. And the butterfly pattern, which appears for traditional hexagonal honeycomb only under biaxial loading, is also observed for the MHH under uniaxial compression. The relative size of the nodes among cell walls is believed to play a crucial role on the appearance of the pattern transformation of the honeycomb structure. This work has revealed the underlying physical mechanism for pattern transformation of honeycomb structures, and would also extend the application range of honeycomb structures to the design of elastic dampers, bending/torsion actuators, or robot drive joints. [ABSTRACT FROM AUTHOR]

• The proposed auxetic honeycomb possesses more excellent auxetic behavior and specific energy absorption than the conventional honeycomb. • The interaction between the structural parameters is analyzed. • The multi-objective optimization of the enhanced auxetic honeycomb (EAH) was investigated. • The theoretical model and Box-Behnken Design model were used to predict the mechanical properties of EAH. In response to the challenge of low stiffness and energy absorption capacity, various designs of negative Poisson's ratio (NPR) structures have emerged. However, these designs often lack a comprehensive analysis of other mechanical properties, leading to subpar mechanical performance. Previous studies have explored the mechanical properties response of enhanced re-entrant honeycombs (ERH) under impact conditions, revealing limitations in optimizing the structure's performance with a single objective. Therefore, this study aims to enhance ERH structural parameters to achieve superior mechanical performance through theoretical derivations and geometric optimizations. The results demonstrate that the proposed theoretical model is consistent with finite element analysis and response surface (RS) predictions. Expressions for Young's modulus, specific energy absorption, and compressive strength are proposed, facilitating the identification of structural parameters that meet specific requirements during reverse design. Furthermore, a multi-objective optimization approach optimizes the geometric parameters based on maximum energy absorption and compressive strength. The mechanical behavior of the optimized ERH is investigated using the finite element method, revealing the energy absorption capacity of 13.78 J/g while maintaining Poisson's ratio at -1.06. Additionally, the deformation mode of the optimized structure showcases enhanced stability compared to traditional honeycomb structures. The theoretical model and RS method were used to guide the design of ERH and promote the application of NPR structures. [ABSTRACT FROM AUTHOR]

• Innovative metamaterial design approach proposed to improve energy absorption capacity. • Varying the structural parameter (D/d) enhanced the metamaterial auxetic effect. • HPH metamaterials absorb energy effectively horizontally with their honeycomb structure. • HPH metamaterials show excellent reusability at lower compression ratios. Hexagonal perforated honeycomb (HPH) metamaterials were designed, fabricated and investigated in this work. Initially, the mechanical properties and deformation modes of various proposed HPH metamaterials (HPH-U, HPH-1 L and HPH-3 L) under quasi-static vertical compression were analyzed using experimental and finite element methods. The findings reveal significant improvements in mechanical properties and energy absorption due to the honeycomb and hierarchical expandable design. Notably, the auxetic effect is diminished. Subsequently, the impact of key dimensional parameters on the mechanical properties and Poisson's ratio behavior was explored. The results highlighted that an increase of elliptical perforation major axis to minor axis ratio enhanced the auxetic effect but compromised load-bearing and absorptive capacity. Additionally, HPH metamaterials displayed exceptional performance under quasi-static horizontal compression, with their honeycomb structure enabling them to withstand both vertical and horizontal impacts while exhibiting excellent energy absorption capabilities. The study also identified relative density as a crucial factor influencing horizontal impact performance. Finally, the study subjected the HPH metamaterials to multiple quasi-static vertical repetitive compressions, meticulously analyzing variations in mechanical properties under diverse compression ratios. Due to distinctive structural design and impressive mechanical properties, HPH metamaterials demonstrate immense potential for applications in automotive engineering and sports protection fields. [Display omitted] [ABSTRACT FROM AUTHOR]

Light composite materials such as auxetic honeycomb structures offer a unique combination of strength, lightweight, and durability, making them ideal for a wide range of industrial and structural applications. Consequently, it is crucial to study the effect of these materials on the dynamic behavior of structures. In this study, an analytical solution based on the multiple-scale method has been proposed to solve equations of motion of a multilayer axisymmetric annular plate. The plate includes two top and bottom isotropic layers and one auxetic honeycomb core layer. By considering both radial and transverse deflections, the governing equations are derived based on the first-order shear deformation theory. The radial and transverse frequencies of the plate are determined from the order zero of equations and a correction coefficient for each frequency has been extracted from the order one and solvability conditions. The response of the plate under harmonic transverse excitation has been determined analytically and by conducting a parametric study, the effect of different geometrical and mechanical parameters on the free and forced vibration responses has been studied. It is observed that employing a honeycomb core in the multilayer plate allows us to significantly decrease the plate weight while the dynamic response and the frequencies remain nearly the same or vary slightly. The results are validated by comparing them with the finite element method and some other references. • An analytical solution for the free and forced vibration of an auxetic composite annular plate is proposed based on the FSDT. • By employing the multiple-scale method, a correction factor for the natural frequencies is determined. • The effect of different combinations of boundary conditions on frequencies is investigated. • The forced vibration lateral and axial responses to a harmonic excitation are determined. • The effect of the auxetic honeycomb layer on the vibration behavior of the plate is studied. [ABSTRACT FROM AUTHOR]

Lightweight materials used for impact mitigation must be able to resist impact and absorb the maximum amount of energy from the impactor. Auxetic materials have the potential to achieve high resistance by drawing material into the impact zone and providing higher indentation and shear resistance. However, these materials must be artificially designed, and the large deformation dynamic effects of the created structures must be taken into consideration when deciding on a protection concept. Despite their promise, little attention has been given to understanding the working mechanisms of high-rate and finite deformation effects of architected auxetic lattice structures. This study compares the static and dynamic elastic properties of different auxetic structures with a honeycomb structure, a typical non-auxetic lattice, at equivalent mass and stiffness levels. In this study, we limit the investigation to elastic material behavior and do not consider contact between the beams of the lattices. It is demonstrated that the equivalent static and dynamic properties of individual lattices at an undeformed state are insufficient to explain the variations observed in impact situations. In particular, the initial Poisson's ratio does not determine the ability of a structure to resist impact. To gain a thorough comprehension of the overall behavior of these structures during localized, high rate compression, the evolution of the elastic tangent properties under compression and shear deformation was monitored, leading to a more profound understanding. Observations made in one configuration of stiffness and mass are replicated and analyzed in related configurations. [Display omitted] • Different lattice architectures are modeled using nonlinear Timoshenko beams. • Auxetic and non-auxetic lattices are compared for static and impact loading. • The lattice geometry is more decisive in impact mitigation than the Poisson's ratio. • Good impact protection is not guaranteed by a high initial Young's modulus. • Maintaining a high lateral pressure wave speed helps to distribute impact energy. [ABSTRACT FROM AUTHOR]

An analytical method is proposed to determine the displacements of a composite cylindrical shell with auxetic honeycomb core layer and variable thickness under combined axial, internal, and external pressures. The thickness and pressure profiles can be arbitrary continuous functions. The displacements are defined in the framework of the first-order shear deformation theory. The composite shell consists of three layers, in which the inner and outer layers are isotropic and the core layer is made of an auxetic honeycomb material. The constitutive equations obey the Hooke law. The equilibrium equations which are a system of coupled differential equations with variable coefficients are extracted by employing the virtual work principle, and they are solved using the matched asymptotic expansion method of the perturbation technique. The effects of different parameters such as the geometry, honeycomb structure parameters, different load profiles, and the thicknesses on the results are studied. The results are compared with the finite element method and some other references. [ABSTRACT FROM AUTHOR]

Finding a non-destructive characterization method for cellular ceramics' compressive strength and fracture behavior has been a challenge for material scientists for years. However, for transparent materials, internal stresses can be determined by the non-destructive photoelastic measurements. We propose a novel approach to correlate the photoelastic stresses of polymer (epoxy resin) prototypes with the mechanical properties of ceramics (alumina). Regular and inverse epoxy honeycombs were 3D-printed via stereolithography with varying structure angles from −35° to 35°, with negative angles forming an auxetic and positive hexagonal lattice. Photoelastic measurements under mechanical loading revealed regions of excess stress, which directly corresponded to the initial fracture points of the ceramic honeycombs. These honeycombs were made by a combination of 3D printing and transfer molding from alumina. The photoelastic stress distribution was much more homogeneous for angles of a smaller magnitude, which led to highly increased compressive strengths of up to 446 ± 156 MPa at 0°. By adapting the geometric structural model from Gibson and Ashby, we showed that we could use a non-destructive technique to determine the compressive strength of alumina honeycombs from the median photoelastic stress measured on similar epoxy honeycomb structures. [ABSTRACT FROM AUTHOR]

• Hybrid re-entrant/hexagonal CF/PA12 honeycombs were 3D printed via FFF. • Temperature-dependent mechanical and piezoresistive characteristics were evaluated. • Hybrid honeycombs excel in enhancing in-plane strength (+64 %) and energy absorption (+125 %). • Hybrid honeycombs exhibit remarkable strain-sensing abilities, boasting gauge factors of ∼146. • The hybrid honeycombs retain 40–60 % of their mechanical properties at 125 °C. This study investigates a novel self-sensing honeycomb composite structure composed of two distinct cellular layers with differing unit cell architectures, specifically hexagonal and re-entrant designs. Short carbon fiber (CF)/polyamide 12 (PA12) composite filaments with 0, 5 or 15 wt.% CF content were utilized to additively manufacture the honeycomb structures via Fused Filament Fabrication (FFF), and their mechanical and piezoresistive self-sensing characteristics were experimentally investigated under quasi-static in-plane and out-of-plane compression at both room temperature and elevated temperatures. The results reveal that the hybrid hexagonal/re-entrant (HR) honeycombs mechanically outperform their non-hybrid double-layer and single-layer counterparts under in-plane loading, reporting an increase in collapse strength and energy absorption by factors of 1.64 and 2.25, respectively. These improvements are attributed to the mechanical interactions occurring at the interface between the auxetic and non-auxetic layers within the hybrid structure, effectively enhancing its structural attributes. Furthermore, the double-layer honeycombs display excellent strain-sensing capabilities within the elastic regime, with gauge factors reaching values as high as 146. Mechanical tests conducted at elevated temperatures reveal that the CF/PA12 honeycombs retain a significant portion of their elastic modulus, strength and energy absorption even at 125 °C, while maintaining high gauge factors of up to 72.4. These honeycombs also exhibit pronounced thermoresistive behavior, evidenced by a decrease in electrical resistance of up to 41.3 % with increasing temperatures from 25 to 125 °C. Considering their exceptional combination of thermo-mechanical, thermoresistive and piezoresistive characteristics, these hybrid double-layered CF/PA12 honeycombs hold promise for potential applications in multifunctional lightweight structures, offering integrated temperature and strain-sensing capabilities. [Display omitted] [ABSTRACT FROM AUTHOR]

• A novel bi-material multistable auxetic honeycomb (BMAH) with reusable and enhanced energy-absorbing phases was designed. • The crushing stress–strain curve shows three stress plateaus, and BMAH maintains a stable Poisson's ratio even at high strain levels, transitioning from near-zero to negative and then to positive. • Under the selected material combination, the second stress plateau is 8 times greater than the first, and the third stress plateau is 17 times greater than the first, significantly improving energy absorption efficiency. • A theoretical model was established to reveal the deformation mechanism of BMAH and predict the plateau stresses and strain range for each deformation stage. • Effects of geometrical parameters and crushing velocity on BMAH stress plateaus and Poisson's ratio were investigated, and a programmable guide for designing stress plateaus and specific energy absorption is presented. The ideal energy absorption structures, in addition to possessing reusability and high energy absorption efficiency, should also possess multiple desired properties to fulfill various functional applications. In this study, a bi-material multistable auxetic honeycomb (BMAH) is fabricated by using bi-material 3D printing technology. Under in-plane crushing, multiple stress plateaus can be achieved and the Poisson's ratio can be stably tuned, allowing for a transition from near-zero to negative and then to positive. The above characteristics are attributed to the specimen's multi-path deformation. The first stress plateau is only associated with recoverable elastic deformation. The second and third stress plateaus, which are 8 times and 17 times higher respectively than the first, are associated with plastic deformation, significantly enhancing energy absorption efficiency. The deformation mechanism is theoretically analyzed, and the effects of geometric parameters on the performance of BMAH are investigated. In addition, the effect of crushing velocity on the crushing behavior of the BMAH is also discussed. As the crushing velocity increases, the total number of stress plateaus transitions from three initially to two and then to one. The developed BMAH exhibits significant potential applications in multi-stage energy absorbers and smart sensors. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to evaluate the dynamic behaviour of sandwich toroidal shells composed of a core with negative Poisson ratio (auxetic honeycomb material) and nanocomposite enriched coating layers under impulsive/periodic pressures considering the geometrical nonlinearity. The set of nonlinear equilibrium equations based on the first-order shear deformation theory are and the resultant nonlinear differential motion equations are approximately solved by the Galerkin method and 4th-order Runge–Kutta solution, respectively. The achieved responses show that the amplitude of outward deformations is intensively increased when the proposed sandwich shells are subjected to rectangular periodic and impulsive loadings which shows the destructive effects of this type dynamic loading. The performed parametric studies shows that these destructive effects can be controlled by changing the geometrical properties of the honeycomb cells and the volume fractions of the nanocomposites in the coating layers. It is notable that in the previous studies the nonlinear dynamic response of toroidal shells subjected to various periodic and impulsive pressures was not investigated. However, in the present work, the mentioned dynamic responses were achieved and investigated without spending time-consuming computational. In fact, the novelty of this work is to develop such a robust and efficient tool. [ABSTRACT FROM AUTHOR]

Flexible piezoelectric sensors have received widespread attention in wearable electronics for their ability to convert mechanical energy into electrical energy, while the insufficient output power and complex preparation process have limited their application. In this work, several honeycomb structures based on graphene macro-film (GAMF) were created via laser engraving, which can utilize negative Poisson's ratio (NPR) properties to improve the output electric performance of flexible piezoelectric sensors. The effect of different electrode materials on the piezoelectric output was investigated in the experiments and compared with the theoretical equations, indicating that the output power of the sensor could be enhanced up to 142 % by improving the materials auxetic mechanical properties. The stability tests have proven that the sensors can operate effectively for a long time under different operating conditions. Moreover, the optimized sensor shows powerful potential for monitoring human movements such as finger tapping, joint bending, and foot stepping. This work opens up a new development path for the preparation of convenient and high-performance wearable electronic devices. The negative Poisson's ratio characteristic of the honeycomb graphene macro-film is used to increase the deformation of PVDF film to increase the electrical output performance of the flexible piezoelectric sensor. The optimized sensor can be used to detect human movements. [Display omitted] • Honeycomb graphene macro-films with different mechanical properties were prepared by laser engraving. • Flexible piezoelectric sensors based on honeycomb graphene macro-films are prepared. • The output performance of piezoelectric sensors can be improved by adjusting mechanical properties of electrode materials. • The flexible piezoelectric sensors can be used to detect human movements. [ABSTRACT FROM AUTHOR]

• 3D origami-inspired auxetic honeycomb with omni-directional high stiffness is proposed. • Theoretical models for predicting the elastic mechanical properties of the CFRP composite 3D honeycombs are developed. • The 3D honeycomb can be applied where good load-bearing capacity and obvious auxetic effect are simultaneously desired. • The 3D honeycomb suggests a potential for 3D isotropic auxetic design. Traditional 3D auxetic materials face significant limitations, marked by low stiffness and pronounced anisotropy. To address these challenges, here a new kind of 3D origami-inspired auxetic honeycomb with omni-directional high stiffness is proposed by us. Two simplified theoretical models based on different assumptions are developed to predict structural homogenized elastic properties along the principal axes. Combined theoretical and numerical studies are carried out to reveal the auxetic mechanism and dominated deformation characteristics of the 3D honeycomb. In order to gain a understanding of its elastic anisotropy, directional dependence of structural homogenized Young's moduli, Poisson's ratios and shear moduli are also investigated in detail. A detailed examination of the dependence of structural homogenized Young's moduli, Poisson's ratios, and shear moduli on loading direction is conducted to comprehend its elastic anisotropy. This paper introduces a feasible method for the rapid manufacturing of the 3D honeycomb using high-performance continuous carbon fiber reinforced composite (CFRP) based on hot-pressing molding. Subsequently, the compressive elastic behaviors of CFRP 3D honeycombs are characterized and evaluated through experimental tests. A comparison with traditional 3D auxetic materials reveals the 3D honeycomb's superiority in both multi-axial loading and rapid manufacturing. Additionally, the demonstrative example suggests that the 3D honeycomb can offer nearly isotropic Poisson's ratio of about −0.9. These results not only demonstrate that the 3D honeycomb is an excellent candidate for applications where both good load-bearing capacity and notable auxetic effect are simultaneously desired but also highlight its potential for 3D isotropic auxetic design. [ABSTRACT FROM AUTHOR]

An analytical model is formulated for 2-D periodic negative honeycomb thicken strut re-entrant lattice structures and a modified rounded corner negative honeycomb structure that shows negative Poisson's ratios (NPR). Analytical modeling is done using Castigliano's second theorem, where each beam is modeled using Timoshenko beam theory, considering bending, stretching, and transverse shearing. Elastic modulus and Poisson's ratio have been formulated for both structures in the form of non-dimensional geometrical characteristics, such as length ratios, angles of re-entrant arms, shear correction factor, and the material's Young's modulus and Poisson's ratios. Numerical simulations conducted in ABAQUS-CAE explicit solver validate the analytical model. The effect of the non-dimensional parameters on the qualities of the developed structure is demonstrated. It is observed that the structures with a low curvature ratio have a high fluctuation of Poisson's ratio and Elastic constant when plotted against the other parameters. The slenderness ratio has little impact on Poisson's ratio but significantly influences elastic modulus. It is shown that various needs can be satisfied by customizing the Poisson's ratios and elastic constant of both forms of lattice construction over an extensive range by carefully choosing the geometrical parameters and material. [ABSTRACT FROM AUTHOR]

• Effects of heating and cooling thermal shock on thermally induced vibration (TIV) are explored. • Influence of geometric nonlinearity under heating/cooling thermal shock forms is revealed. • The TIV characteristics of sandwich beams with auxetic honeycomb cores are discussed and compared with traditional honeycomb. • The instability conditions of the clamped beam with immovable ends under heating thermal shock are given. The nonlinear thermally induced vibration (TIV) characteristics of sandwich beams with auxetic honeycomb cores under general boundary conditions are studied. Based on first-order shear deformation theory, the dynamic governing equations are obtained through Hamilton principle, in which geometric nonlinearity and temperature dependence are considered. The temperature field along the thickness is calculated by finite element method and nonlinear TIV responses are solved via Newton-Raphson-Newmark method. The effects of temperature dependency, thermal shock forms, geometric nonlinearity, thicknesses of beam and face-sheet, boundaries and honeycomb geometrical parameters are studied. Results show that the reduction of the absolute inclined angle of the auxetic honeycomb can weaken the TIV responses. The influence of geometric nonlinearity on quasi-static and dynamic responses depends on the thermal shock form. Thermal buckling is the necessary condition for the occurrence of the TIV in clamped beams with immovable ends. Moreover, the research provides some design references to suppress the TIV responses of the sandwich beam with auxetic honeycomb core. [ABSTRACT FROM AUTHOR]

Auxetic lattice structures are known for their superior stiffness-to-density and strength-to-density ratios. Re-entrant hourglass exhibits an acceptable equivalent elastic modulus and remarkable energy absorption capacity among various auxetic configurations due to their flexibility and hinge deflecting during crushing loads. This study introduces a curved hourglass honeycomb which can be produced using 3D printing with pure or reinforced filaments incorporating continuous fibers. New closed-form formulations are analytically derived using an energy method by considering an extracted unit cell to predict the equivalent in-plane mechanical properties for the first time. The plateau stress of the proposed honeycomb is evaluated at the densification state of a unit cell using the energy conservation theory, equating external work with plastic energy dissipation. The accuracy of these extended relations is validated against experimental outcomes, demonstrating good agreement between analytical and experimental results. Additionally, robust linear and nonlinear finite element analyses are conducted to assess the accuracy of the obtained relations, including the equivalent stiffness and plateau stress for structures produced with reinforced filaments. The nonlinear finite element code employs appropriate subroutines to model plasticity/damage events. Based on the established analytical relations for stiffness and plateau stress, multi-objective optimization using Genetic Algorithm is applied to define optimum values for the Pareto front chart's objective functions of stiffness and plateau stress. The optimization process involves exploring the design space and defining the values of geometrical parameters to achieve the desired objectives. In conclusion, this study presents a novel approach to developing curved re-entrant honeycomb structures, with analytical formulations validated against experimental and numerical results. Optimization helps to identify optimal configurations concerning stiffness and plateau stress, offering potential applications in lightweight and high-strength materials design. According to the obtained results, for selection of the best value for curved strut angle which results in the optimum value of stiffness and plateau stress, a range between 10°-34° can be considered depending on the volume fraction of fibers. [ABSTRACT FROM AUTHOR]

Recently, auxetic metamaterials have turned into an area of growing interest, because of their deformation uniqueness, design flexibility, and functional diversity. To achieve their programmable design of densification and energy absorption, the variable stiffness factor method (VSF) emerged. However, the energy absorption capacity of the metamaterials designed by this method has a significant reduction. In this work, to remedy this defect, several different lightweight specimens are proposed and fabricated to extend the stage of energy absorption and retain the tunability. Then quasi-static compression tests and finite element methods are carried out to analyze the mechanical properties of the designed boundary-constrained structure (BCS) and X-shape constrained structure (XCS). The accuracy of the densification points and energy absorption capacity of the two structures at different VSF values are also studied. The results show that the densification points of the designed structures can be adjusted quantitatively, and their deformation modes are more stable than conventional structures during compression. Furthermore, their specific energy absorption is four and five times higher than that of non-lightweight structures with VSF = 40%, respectively. These findings contribute to advancing the implementation of auxetics in applications of multistage protective structures. • A lightweight metamaterial based on the variable stiffness factor (VSF) method is proposed. • The proposed structures realize multi-level energy absorption and stable deformation. • The SEA of proposed structures was 4 and 5 times higher than that of VSF = 40% structure. [ABSTRACT FROM AUTHOR]

Modern engineering extensively employs complexly curved shell structures, presenting mathematical challenges in analyzing their mechanical behavior due to geometric intricacies. The recent trend of incorporating advanced lightweight materials into these structures drives the need to develop improved theories and methods. This study presents an investigation into the free vibration analysis of barrel-shaped sandwich (BSS) shells using a modified thick shell theory (MTST). These sandwich shells feature functionally graded (FG) ceramic-metal layers on both inner and outer surfaces, with a lightweight honeycomb core. Notably, the honeycomb layer's thickness surpasses that of the inner and outer layers, necessitating the application of thick shell theory for accurate analysis. However, previous studies have often used classical theories for thin shells, and those applying thick shell theory sometimes neglected the curvature effects in the fundamental equations and rotary inertia components. Thus, this research employs the MTST to overcome these limitations. The study includes comparative validations and explores the impact of material parameters and curvature radii on the natural frequencies of these barrel-shaped sandwich shells through numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, an analytical investigation is presented on the natural frequency analysis of sandwich plate resting on Winkler-Pasternak type elastic foundations in thermal environment. The sandwich plate consists of an auxetic honeycomb core with negative Poisson's ratio, which is assumed to perfectly bond to two carbon nanotube reinforced composite (CNTRC) face sheets to ignore potential interface effects or imperfections in bonding. The material properties of CNTRC are assumed to be temperature dependent. The volume fraction of carbon nanotube (CNT) varies through the thickness dimension according to linear functions with five different distribution patterns of CNT including UD, FG-O, FG-V, FG-Λ and FG-X. The governing equations of motion are derived based on the Reddy's first order shear deformation plate theory and Hamilton's principle, and the expression of the natural frequency is performed via Galerkin method. Artificial neural network (ANN) model is established to accurately predict the natural frequency of the sandwich plate on the basis of 1450 data points collected from analytical results. The effects of various material and geometrical parameters on the natural frequency of the sandwich plate are investigated in details. [ABSTRACT FROM AUTHOR]

In this study, a model for the nonlinear dynamic analysis of the geometrically imperfect sandwich beam with functionally graded material (FGM) facets and auxetic honeycomb core is proposed. The auxetic feature of the honeycomb material is realized by a homogenization method, which gives the expressions of the effective material coefficients in terms of material property and cellular geometric parameters. The nonlinear motion equation of the geometrically imperfect beam is derived based on the Reddy's higher shear deformation theory, von Kármán nonlinear theory, as well as general geometric imperfection function. The thermal effect on the material properties and structural rigidity is also taken into account in this model. The Newmark method and Newton–Raphson iterative method are employed to solve the nonlinear motion equation of the sandwich beam. In numerical examples, the dynamic response of the sandwich beam under two types of load, i.e. moving load and impulse load, are discussed in details. The influences of various factors (such as material parameter, geometric imperfection, and thermal condition) on the nonlinear dynamic behaviors of the sandwich beam are elaborately investigated. The numerical results show those factors can play significant roles in the bearing ability, structural stiffness, or nonlinear dynamic behaviors of the sandwich beam in certain conditions. Some key conclusions on the influences are drawn from the numerical results, which can be a useful reference for future investigations. [ABSTRACT FROM AUTHOR]

This study is the first of its kind to apply an analytical technique to offer an accurate solution for the static buckling and static bending of functionally graded (FG) sandwich nanobeams, in which the core layer is an auxetic honeycomb. One notable aspect of this work is the use of third-order shear deformation theory for the computations. It is worth noting that the displacement field of the nanobeam is contingent upon a single parameter. This approach enables the resolution of stability and static bending issues encountered in nanobeams including auxetic honeycomb cores, while also providing a realistic depiction of the beam's mechanical behavior. The two surface layers are composed of different materials, each of which has mechanical characteristics that change in accordance with the exponential function law. The precise solution described in this work is very adaptable and may be used to investigate the mechanical behavior of beams with different boundary constraints, taking into consideration the effect of the nonlocal parameter. When the angle α of the cell varies, the honeycomb core's mechanical characteristics, such as Poisson's coefficient and elastic modulus E , vary continually. This results in static bending and buckling responses that are distinct from those of other auxetics. This study also found it intriguing that the wall angle α has a value of around 90° and that sandwich nanobeams have the highest load capacity. In addition, numerical calculations have been performed to demonstrate the influence of certain geometrical parameters, materials, and boundary constraints on the critical buckling load and maximum deflection of the nanobeam. • This study is the first of its kind to apply an analytical technique for the static buckling and static bending of FG sandwich nanobeams, in which the core layer is an auxetic honeycomb. • This study offers calculation findings demonstrating the effect of geometrical factors, materials, and boundary conditions on the ultimate load response and maximum displacement of FG sandwich nanobeams. • It is discovered that a certain value for the wall angles of the core layer cell yields the highest possible performance from this beam. [ABSTRACT FROM AUTHOR]

Auxetic structures, which have a negative Poisson's ratio, have good mechanical energy/impact absorption properties. These structures have found application in sandwich composites in the aerospace and defence industries, in the production of armour or protective sports equipment. In this study, the mechanical behaviour of the auxetic honeycomb structure in different directions (in-plane and out-of-plane) under impact loading was investigated. For the in-plane (x and y) and out-of-plane (z) directions, boxes with an auxetic honeycomb structure were produced by material extrusion method using Power ABS filament. In the experimental study, dynamic tests were carried out with a drop test machine. Besides, explicit analyses were performed by creating finite element models for these 3 directions. The experimental and numerical results have shown that the energy absorption property of auxetic honeycomb geometry is superior in the case of out-of-plane loading, in agreement with each other. In in-plane loadings, crush force efficiency (CFE) and crush forces were lower. [ABSTRACT FROM AUTHOR]

3D printable multi-material honeycombs have attracted increasing interest recently due to the improved elastic moduli, buckling and energy absorption properties. This paper proposes an analytical homogenization for the equivalent in-plane elastic moduli (EIEM) of multi-material honeycombs. First, the axial and bending stiffness of a cantilever beam consist of three sections made of different materials is formulated. Then based on unit cell method and cantilever beam model, the closed-form expressions of EIEM are proposed by fully considering the deformations of both joints and cell walls with arbitrary stiffness, which are sufficiently general to be applied to hexagonal, auxetic and rectangular multi-material honeycombs and validated very well by numerical simulations and experiments. Furthermore, the effects of geometric and material distribution ratios on EIEM are discussed. The results show that the geometric and material distribution ratios of inclined cell wall have a significant effect on all five EIEM while that of vertical cell wall shows a significant effect on shear modulus but only a slight effect on y- direction elastic moduli. Compared with single-material honeycombs, changing joint stiffness has a significant effect on the equivalent Young's moduli and shear modulus but a slight effect on Poisson's ratios. • Closed-form expressions of equivalent elastic moduli for multi-material honeycombs. • Axial and bending stiffness formulated for a dual-material cantilever beam. • Analytical expressions of moduli match well with numerical and experimental results. • Dependency of material and geometric distributions on moduli investigated. • Proposed method applied to multi-material hexagonal and auxetic honeycombs. [ABSTRACT FROM AUTHOR]

• A novel auxetic honeycomb (NAH) combined with chiral and re-entrant was proposed. • The EA and SEA of NAH are improved under Quasi-static compression and impact. • Under high-velocity impact, the EA of NAH is better than hexagonal honeycomb. • NAH with thickness gradient shows obvious auxetic behavior under high-velocity impact. Auxetic metamaterials as a cutting-edge field have attracted extensive attention from researchers because of their peculiar deformation mode and excellent mechanical properties. However, the unstable deformation and low stiffness of auxetic structure limit their potential development. To address these limitations, a novel auxetic honeycomb (NAH) has been proposed by combining an original re-entrant hexagonal honeycomb (RH) with cross-chiral honeycomb (CH). The proposed structure has higher stiffness than RH, and more stability than CH. Additionally, the stiffness, densification point, and auxetic behavior can be adjusted by the angle of cell ribs (θ). In this study, the static mechanical properties and deformation behavior of NAH are investigated experimentally and numerically. Furthermore, the energy absorption and deformation behavior of NAH under different impact loadings (low-, medium- and high-velocity) are investigated numerically. Finally, a series of functionally graded NAHs with varying thicknesses are studied to improve the impact resistance of NAH. The results show that NAH has better specific energy absorption than RH and CH under static compression. Moreover, NAH with θ < 90 ° exhibits greater energy absorption capacity compared to NAH with " θ > 90°" at high-velocity impacts. [ABSTRACT FROM AUTHOR]

Lantern, also known as coloured-lantern making, is known for being an ancient traditional craft in China that can be dated back as early as West Han Dynasty. Inspired by the lantern, the lattice element is built by vertically rotating and duplicating the 2D units, then the 3D auxetic metamaterial is formed by connecting the 8 ligaments of the lattice element on two perpendicular planes. As the elastic behaviors associated with this metamaterial are still almost unknown to a large extent, in this study, an analysis has been conducted to investigate how the geometric parameters related to the lattice design influence its elasticity. For this reason, a novel 3D lantern-shaped honeycomb structure (LSH) has been proposed, the Castigliano's second theorem, energy principle, and Moore's theorem are utilized to solve its Young's modulus and Poisson's ratio in the three main directions. The theoretical results exhibit good agreement with the numerical and experimental results. The results showed that the elasticity of LSH structures can be programmed by adjusting a range of geometric parameters. In addition, LSH features a bidirectional zero Poisson effect and a good stress distribution during compression. It shows potential in terms of load-bearing to meet the requirement of lightweight and high stiffness. This structure shows good promise for applications in aerospace, construction and other fields. [ABSTRACT FROM AUTHOR]

• The free vibration and nonlinear dynamic response of sandwich plates with an auxetic honeycomb core and piezoelectric face sheets are freshly addressed. • An analytical solution based on the first-order deformation plate theory and von Karman-type nonlinear strain-displacement relationship is established for movable simply supported and immovable simply supported plates. • The Galerkin and Runge–Kutta fourth-order methods are used to solve the system of nonlinear differential equations and capture the displacement-time and acceleration-displacement curves. • New parametric studies regarding the influence of the material, geometrical parameters, and elastic foundation coefficients, the geometrical parameters of the auxetic honeycomb core layer, as well as the electric boundary condition on the free vibration and nonlinear dynamic response of piezoelectric-auxetic sandwich plates are examined. This article analyses the nonlinear dynamic behavior and the free vibration of a piezoelectric auxetic honeycomb sandwich plate resting on a Pasternak elastic substrate. The plate includes two face sheets of piezoelectric material and an auxetic honeycomb core with a negative Poisson ratio. The first-order shear deformation plate theory, together with the von Kármán type nonlinear strain-displacement relationship, is used to establish the nonlinear equations of motion. Linear electric potential change with piezoelectric layer thickness is assumed. Two types of boundary conditions, namely immovable and movable simply supported, are considered. The displacement-time and acceleration-displacement curves under dynamic loads are determined by using the Galerkin and Runge-Kutta fourth-order methods. Verification examples have been performed and confirmed the accuracy of the model. Finally, several novel investigations have been conducted to evaluate the effect of material, geometrical parameters, and elastic substrate coefficients on the frequency and nonlinear dynamic characteristics of piezoelectric auxetic honeycomb sandwich plates for both open-circuit and closed-circuit operation. [ABSTRACT FROM AUTHOR]

Mechanical metamaterials represent a class of deformable systems, which exhibit macroscopic deformations, mechanical, and/or thermal properties. These emerge due to the structure of their subunits rather than their materials composition and typically exhibit anomalous (normally negative) macroscopic structural, mechanical, or thermal property/properties caused by a change in shape/size of the system. Herein, a class of honeycombs is discussed, which push to the extreme the classical definition of "mechanical metamaterials," exhibiting temperature‐tunable Poisson's ratio properties. More specifically, centrosymmetric honeycombs with T‐shaped joints constructed from different materials are shown to exhibit temperature‐dependent Poisson's ratio values, which can be either positive or negative (auxetic) depending on the external stimulus the system is subjected to. The sign and magnitudes of the Poisson's ratio values are explained in terms of particular geometries that these composite honeycomb systems attain at different temperature conditions. In particular, auxeticity is attributed to the transformation of the T‐shaped units to re‐entrant units. Practical aspects on how these properties may be achieved are discussed, including the possibility that the changes in shape, and hence Poisson's ratios, are induced via different extents of dryness on opposite surfaces of ligaments made from absorbent materials. [ABSTRACT FROM AUTHOR]

Honeycombs or foams with reentrant microstructures exhibit effective negative Poisson's ratio. Although they are light weight due to inherently empty space, their overall stiffness and damping are somewhat limited. With judiciously chosen filler material to fill the voids in star‐shaped honeycomb, it is numerically demonstrated its auxeticity may be enhanced. By combining the filler and skeleton, the hierarchical composite materials are constructed. The magnitude of the enhancement depends on inner and outer filler's modulus mismatch, as well as the types of filling. Filler's auxeticity also largely enhances overall auxeticity of the outer‐ and all‐filled honeycomb. In addition, for outer‐filled honeycomb, its effective viscoelastic modulus and damping are significantly increased, while maintaining relatively light weight, due to local stress concentration. [ABSTRACT FROM AUTHOR]

In this paper, the thermal shock resistance of an auxetic ceramic honeycomb plate is studied based on the fracture mechanics concept for the cases of a central crack or an edge crack. The transient temperature field and transient thermal stress field are obtained for both auxetic and non-auxetic structures. The relationship between the thermal stress intensity factor (TSIF) and the internal cell angle, crack length and time is determined and the critical temperature for the initiation of crack propagation is predicted. Results show that compared with the non-auxetic ceramic honeycombs which are at an internal cell angle of 30°, the critical temperature of the auxetic ceramic honeycombs whose cell are orientated at an angle of −30° increases by 78.5% and the TSIF at the crack tip decreases by 40%, respectively. Hence, the auxetic structures have better thermal shock resistance. This study indicates that auxetic ceramic honeycombs have significant potential applications in harsh temperature environments. [ABSTRACT FROM AUTHOR]

The nonlinear mechanical responses of tetrachiral honeycombs under large deformation are theoretically analyzed by employing elliptic integrals, and the results are verified by numerical simulations. The nonlinear relationships between normal stress, shear stress, Poisson's ratio and the strain are derived for the tetrachiral honeycombs. It is found that the Poison's ratio of the tetrachiral honeycombs under large deformation is totally different from that under small deformation. The Poisson's ratio can achieve to a large magnitude of 0.8 in the former case, while remains 0 in the latter case. Moreover, the tetrachiral honeycombs exhibit positive Poison's ratio under large tensile-deformation, whilst showing negative Poisson's ratio under large compression-deformation. The magnitude of Poisson's ratio depends on both the honeycomb's deformation and the ligament relative length, while it is insensitive to the ligament thickness. Besides, the coupling effect between tensile (or compression) and shear is observed for the tetrachiral honeycombs. In other words, shear deformation appears within the honeycomb under uniaxial loading. The coupling effect depends on both the honeycomb's deformation and the geometric parameters of the cell structure. And the quantitative relationships among them are derived. This special coupling effect of tetrachiral honeycombs provides a new idea for designing more metamaterials. [ABSTRACT FROM AUTHOR]

• In-plane crushing responses of the tetra-chiral (TC) honeycombs were investigated by using experimental and numerical methods. • Theoretical formulas were derived to predict plateau stresses of the TC honeycomb under both quasi-static and dynamic crushes. • Effects of unit cell radius ratio on crushing strength, dynamic sensitivity index and effective Poisson's ratio (EPR) of the TC honeycomb were investigated. • Stress and EPR evolutions of the TC honeycomb with different orthogonal array ratios were also investigated. Tetra-chiral (TC) honeycombs are a type of auxetic materials showing negative Poisson's ratio (NPR), which are promising for impact energy absorption. This study aims to analyze the in-plane crushing response of the TC honeycombs under both quasi-static and dynamic loading conditions through numerical simulations and theoretical analyses. The numerical modeling techniques in LS-DYNA were validated using the quasi-static crush test data of TC honeycomb specimens obtained with a 3D-printer. Numerical simulations revealed the "Z" mode deformation and the "bulge effect" under quasi-static crushing, and the row-by-row "I" mode deformation under dynamic crushing of the TC honeycombs. By referring to the simulation results, theoretical models were derived based on the representative unit for predicting the TC honeycomb's crushing strength, i.e. plateau stress, under both quasi-static and dynamic loads. Good agreement was found between the theoretical and the numerical predictions with a maximum relative error of 7%. Parametric analyses showed that the unit cell configuration has a great effect on the crushing strength of TC honeycomb under in-plane crushing. The dynamic sensitivity index was defined to quantitatively evaluate the sensitivity of the TC honeycomb's crushing strength to the loading speed, and was found to depend on the unit cell geometry. The TC honeycomb was found to present a varied effective Poisson's ratio (EPR) with strain under both quasi-static and dynamic in-plane crushing; smaller radius ratio and lower crushing speed were found to yield more obvious NPR effect. Moreover, relative dimension of the TC honeycomb represented by the orthogonal array ratio do not affect its plateau stress under either quasi-static or dynamic crushing, while large orthogonal array ratio results in more obvious "bulge" and NPR effects under quasi-static crushing. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Re-entrant anti-trichiral honeycomb is a typical auxetic material. The collapse process can be divided into three stages while its negative Poisson's ratio (NPR) effect under large deformation is still unclear. In the present paper, the NPR effects of re-entrant anti-trichiral honeycombs under large deformation are studied by numerical and theoretical method. Numerical results are verified by the experiments with respect to their deformation mechanism and stress-strain behavior. Theoretical formulas are derived to predict the NPR effect of the honeycomb under large deformation. The analytical predictions are in good agreement with the FEM results. It is revealed that the NPR effect of the honeycomb is magnified with the global strain in the second stage while is weaken in the third stage of the deformation process. The decrease of the ligament-ratio and the mean radius will result in more obvious NPR effect. Variation of cell-wall thickness doesn't have much impact on the Poisson's ratio in the second stage, while smaller cell-wall thickness will induce larger NPR in the third stage. The present work is supposed to shed light on the design and fabrication of re-entrant anti-trichiral honeycombs with desired Poisson's ratio. Image 1 • Analytical predictions of the NPR effect under large deformation exhibits a good agreement with the numerical results. • A special deformation mechanism and stress-strain behavior are illustrated by the experiments and numerical simulations. • The negative Poisson's ratio (NPR) of the honeycombs varies differently with strain at different stages. • Variation of cell-geometry parameters greatly influence the NPR effect of the honeycombs. • More evident NPR effect is exhibited when the honeycomb gradually develops into the conventional re-entrant honeycomb. [ABSTRACT FROM AUTHOR]

• The proposed hybrid AuxHex structure consists of auxetic and honeycomb cells. • The equations for modulus and strength along x - and y -directions are derived. • Theoretical results are in agreement with simulation and experimental results. • Mechanical properties and specific energy absorption are enhanced 16% and 38%. The architected mechanical metamaterials have garnered significant research attention for a variety of engineering application due to their remarkable mechanical properties and unique deformation behavior. Herein, the in-plane uniaxial compressive response and energy absorption capacity of a novel hybrid configuration, AuxHex structure, which consists of auxetic and hexagonal honeycomb cells, are systematically investigated through theoretical, finite element simulation and experimental methods. A series of AuxHex sandwich core panels have been fabricated with nylon material by using additive manufacturing route. The relationships for Young's modulus and plastic collapse stress along different loading directions are derived and validated through the comparative analysis. In addition, the deformation mechanism and failure modes of the AuxHex structure have also been discussed in detail. The AuxHex structures have exhibited superior Young's modulus, collapse strength and energy absorption than traditional honeycomb structures. In the x -direction, the energy absorption capacity was improved by 38%, which can be attributed to the uniform and stable deformation mode of the unit cell. The theoretical prediction results of Young's modulus and plastic collapse stress are consistent with finite element simulation and experimental results. The AuxHex structures demonstrate a novel design strategy for the architected metamaterials through the combination of various cellular cells. The hybrid structures will play an important role in both the load-bearing and energy-absorbing applications, and it demonstrates a novel design strategy for the architected metamaterials through the combination of various cellular cells. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Auxetic structures have theoretically superior bending resistance that was previously inaccessible. Compared with the planar two-dimensional (2D) auxetic structures, the three-dimensional (3D) counterparts may exhibit auxetic behavior in multiple directions. Recently, increasing studies have been devoted to studying the mechanical properties of 3D auxetic structures. In this paper, two 3D honeycomb structures were proposed, namely 3D re-entrant honeycomb and 3D hexagonal honeycomb. Subsequently, the mechanical properties, deformation modes, and deformation mechanisms of these two honeycomb structures under three-point bending were investigated experimentally and numerically. Compared with the 3D non-auxetic hexagonal honeycomb, the 3D auxetic re-entrant honeycomb exhibits higher ductility and fracture resistance. In addition, unlike the conventional honeycomb structure, the mid-span section of the 3D auxetic honeycomb exhibits a trapezoidal deformation mode under bending. Finally, the influence of the number of unit cells and geometric parameters on the mechanical properties of the 3D honeycomb structure were systematically studied by parametric analysis. The excellent bending performance provides a basis for the application of auxetic honeycomb in the fields of biomedicine, soft robots, and buffer devices. [Display omitted] • Two 3D honeycomb structures, namely 3D auxetic honeycomb and 3D non-auxetic honeycomb, were designed and fabricated. • The mechanical properties, failure modes, and deformation mechanism of two specimens are investigated under three-point bending. • Compared with the 3D non-auxetic honeycomb, the 3D auxetic honeycomb exhibits better ductility and a trapezoidal deformation pattern at midspan. [ABSTRACT FROM AUTHOR]

Highlights • Fracture behavior of auxetic cellular structures is investigated. • A ductile damage computational modeling technique is presented. • Identification of ductile damage material parameters is given. • The influence is evaluated of the shape of unit cells on fracture behavior. • Experimental testing is carried out to validate the numerical results. Abstract Auxetic cellular structures are advanced materials with negative Poisson's ratios, which exhibit some unique features which are useful for various applications. The objective of this paper is the numerical simulation and experimental analysis of evolution propagation under quasi-static loading conditions in selected auxetic cellular structures with different geometries and orientations of unit cells that is: (i) honeycomb structure, (ii) re-entrant structure, and (iii) rotated re-entrant structure. The failure modeling capability of Simulia Abaqus code for ductile materials is used for the numerical simulation. The paper presents in detail the calculation methodology for determination of ductile damage material parameters that, are used for further numerical simulations of the damage initiation and evolution. Standard Compact Tension (CT) specimens are selected for the numerical simulation and experimental testing. Here, the specimens are made from 7075-T651 aluminum plate, cut using water jet cutting technology. Using a numerical approach, the fracture behavior of the selected auxetic structures is estimated first. Experimental testing is also carried out to validate the numerical results. The comparison between computational and experimental results regarding crack propagation path and force-displacement diagrams showed a reasonable agreement. [ABSTRACT FROM AUTHOR]