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• The effect of thickness and reinforced strut gradients on the crushing response of RRH is explored. • Two plateau stresses of RRH specimens are derivated theoretically with a relative error of less than 7 %. • Both thickness and catenary gradients inspire a multi-step deformation mode and multi-plateau stress. • Some suitable thickness and catenary gradients are discovered under different impact velocities. Re-entrant honeycombs have demonstrated promising applications in engineering fields attributed to better manufacturability and adaptability. Herein, the reinforced re-entrant honeycombs (RRH) with thickness and reinforced strut gradients are proposed, respectively, and their in-plane energy absorption is investigated through experiment, theoretical analysis, and simulation. Metallic specimens of uniform and graded RRH are manufactured through a step-by-step method. The deformation mode and plateau stress (PS) of these specimens are significantly influenced by both thickness and catenary gradients. Two PSs of RRH specimens are predicted theoretically with a relative error of less than 7.0 %. Subsequently, the deformation mode and energy absorption of uniform and graded RRH, subjected to varying load rates, are investigated thoroughly with a numerical method verified against the experimental data. The results show that both thickness and catenary gradients can inspire multi-step deformation mode and prevent instability deformation. Compared to uniform RRH (U-RRH), the specific energy absorptions (SEA) of thickness gradient (TG)-123 (123 represents that the thicknesses from impact end to fixed end are t 1 , t 2 , t 3) and TG-213 are enhanced by 52.2 % and 49.8 %, respectively, under quasi-static compression, the SEA of TG-132 and TG-123 are raised by 41.6 % and 20.2 %, respectively, under low-velocity impact, and the SEA of strut gradient (SG)-123 is 66.7 % higher than that of U-RRH under high-velocity impact. More significant auxetic deformation does not always mean better energy absorption because there is also an increased tendency of global instability and earlier densification points. This work provides a novel approach to designing high-energy absorption honeycombs with low structural complexity. [ABSTRACT FROM AUTHOR]

• Thermal-force external coupling enhances polyimide molecular chain orientation. • Orientation modulation increases the honeycomb shear strength 10 times to 1.07 MPa. • Excellent thermal performance of polyimide aerogel honeycomb (T d5% >650 °C). • Fabricating integrated lightweight honeycomb structures using the formwork method. Lightweight honeycomb structures are widely used in applications that require high strength-to-weight ratios and low densities, including aircraft, automobiles, and various engine components. However, due to the immaturity of microstructure conditioning techniques and the fact that highly porous structures usually fracture during stretching, it is challenging to obtain both high-strength and lightweight porous structures. Herein, a newly developed multilayer interconnected polyimide aerogel-based paper honeycomb is successfully prepared based on the ice crystal reverse template method and multi-level structure regulation via chemical and physical interactions. The synergistic effect of the hot extrusion-stress strategy and the heat imidization process provides the submicron layer of the paper honeycomb wall with more orderly molecular chain stacking, excellent orientation, and an enhanced folding degree between layers. The prepared polyimide aerogel paper honeycombs have low density (approx. 8–9 kg/m3), good shear strength of 1.07 MPa (W direction) and 0.86 MPa (L direction), excellent specific compressive strength (0.38 MPa), and excellent thermal stability. These integrally molded polyimide paper honeycombs, as sandwich resin-based composite structures, provide a new versatile platform for aerospace and marine applications. [ABSTRACT FROM AUTHOR]

• The novel helical layered square honeycombs exhibit higher strength (∼176 %) and specific energy absorption (∼502 %) than regular square honeycomb. • The quasi-static compressive behaviors of helical-layered and regular square honeycombs are compared. • The deformation modes of helical-layered square honeycombs are dominated by the relative density and the number of helical layer. • The mechanical properties and energy absorption capacity improved by increasing the number of helical layer. • The failure mechanisms of helical-layered square honeycombs are dominated by layer cracking. Bionics shape design of cellular structures has the potential advantage of improving their both mechanical properties and energy absorption capabilities to the conventional honeycomb structures. In this article, inspired by square porous wood and DNA double helix, we demonstrate the creation of the novel helical layered square honeycombs (HLSHs) that simultaneously exhibit high strength and excellent energy absorption capacity. In-plane compression experiments and finite element simulations revealed that helical structure can effectively strengthen every unit cell to resist local stress concentration which always leads to rapid strain localization and finally followed by catastrophic collapse. Furthermore, the stiffness, strength and energy absorption capability can be continuously improved by increasing the number of helical layers. More specifically, the HLSH-4L (4 layers) exhibits higher collapse stress (∼176 %) and specific absorption energy (∼502 %) compared with that of regular square honeycomb (RESH). The investigation of deformation and failure behavior show that the helical structure can supply high cell-buckling resistance and facilitate the "X" shape deformation band. Besides, the helical structure also caused the transition of failure mechanisms from printing fibers tearing in RESH to layer cracking in HLSHs. This study can present insight into the design of lighter and stronger honeycomb. [ABSTRACT FROM AUTHOR]

This study presents a novel three-dimensional orthogonal accordion structure (3D-OAS) with multi-directional zero Poisson's ratios (ZPR) achieved by combining two-dimensional accordion honeycomb structures (2D-AHS) orthogonally. The analysis of its mechanical performance involved deriving equivalent elastic properties using beam theory. Subsequently, a three-dimensional Cauchy equivalent model (3D-CEM) was established using the variational asymptotic method to convert structural orthotropy into material orthotropy. Uniaxial compression tests were conducted on unit-cell and multi-layer 3D-printed specimens to confirm the multi-directional ZPR effects. The in-plane and out-of-plane static behaviors of 3D-OAS panels were evaluated, affirming the accuracy and effectiveness of the equivalent model. Numerical simulations showed that the 3D-CEM required fewer elements and nodes, representing 0.85% and 0.83% of the computing time required by 3D FE model for in-plane and out-of-plane deformation analyses, respectively. The 3D-OAS panel experienced no significant vertical deformation during in-plane tension but exhibited cylindrical deformation with ZPR characteristics under out-of-plane bending. Specifically, normal stresses exceeded shear stresses at the intersection of the two perpendicular horizontal struts. The inclined angle of strut minimally influenced the Poisson's ratio of 3D-OAS but notably impacted the elastic moduli. These findings provide important theoretical support for the design and application of three-dimensional accordion honeycomb structures. • 3D-OAS achieves multi-directional ZPR effects through orthogonal combination. • Mechanical analysis involves deriving equivalent elastic properties. • 3D-CEM transforms structural orthotropy into material orthotropy. • Uniaxial compression tests on unit-cell and multi-layer 3D-printed specimens. • Efficient 3D-CEM with reduced elements and nodes for numerical simulations. [ABSTRACT FROM AUTHOR]

• Through hypervelocity impact experiments, the impact process was recorded by high-speed camera, and the damage effects of reactive projectile and Al2024 projectile on the aluminum alloy honeycomb sandwich panel double-layer structure were compared. • The damage enhancement mechanism of reactive projectile to double-layer structure was revealed by numerical simulation and theoretical analysis. • The influence of impact-induced detonation reaction of reactive projectile on the "channel effect" of honeycomb sandwich panel was obtained. In this paper, the experiments of Al2024 and reactive projectiles with hypervelocity impact on aluminum alloy honeycomb sandwich panel double-layer structure respectively were carried out by using two-stage light-gas gun, and the impact processes were recorded through high speed camera. According to the analysis of the experimental results, the debris clouds motion process and the damage effects on double-layer structure were compared. The damage enhancement mechanism of reactive projectile was revealed through numerical simulation and theoretical methods. The impact-induced detonation reaction of the reactive projectile can significantly reduce the "channel effect" of the honeycomb sandwich panel by destroying the honeycomb core cell wall, increase the perforation on the back facesheet of the honeycomb sandwich panel, and generate the debris cloud with higher temperature and faster expansion velocity. The debris cloud induced by the reactive projectile has a larger load distribution area on the rear plate, avoiding the concentration of loads in the center of the rear plate, and cause large area impact and thermal combined damage effects on the rear plate and internal space of the double-layer structure, while ensuring that the target structure cannot be penetrated. The reactive projectile efficiently applies the kinetic energy and chemical energy released by the impact-induced reaction to the interior of the target structure, the waste of kinetic energy caused by whole structure penetration can be avoided, resulting in significantly higher damage effects than the inert Al2024 projectile. [ABSTRACT FROM AUTHOR]

• The vibration suppression performance of composite honeycomb hemispherical shells with functional gradient protection coating is studied. • A mathematical model is proposed for predicting the dynamic behaviors of such shells with advanced coating. • The solution principle of the natural characteristics and vibration responses of such coated shells is clarified. • Some important design suggestions are summarized to improve the vibration resistance of such coated shells. The vibration reduction performance of composite honeycomb hemispherical shells (CHHSs) coated with functional gradient protection coating (FGPC) are investigated in this work. Using the first-order shear deformation theory and the power-law distribution rule, the virtual spring technique, the regional decomposition method, and the Newmark-Beta approach, etc., a dynamic model of the FGPC CHHSs under base excitation is formulated to solve the inherent characteristics and displacement responses in time and frequency domains. After a set of convergence analyses are completed to ascertain an appropriate segment number and the stiffness values of virtual springs employed in the predictive model, the forecasted vibration parameters are verified using the literature and experimental results that are performed on uncoated and coated shells. The maximal natural frequency errors of the current model compared to the experimental results are 3.8% and 4.8%, and the displacement response errors under different excitation amplitudes are less than 10.3% and 12.7%, respectively, which demonstrate the correctness of such a model. Finally, the impact of key structural and material parameters on the vibration behaviors of the FPGC CHHSs is evaluated. To improve their vibration suppression capability, it is recommended to choose a high gradient index of coating material and a large thickness ratio of the FGPC to the overall shell with a reasonable moduli ratio of Material A to Material B of the FGPC to improve vibration reduction capability. This study offers a practical model tool and several important design recommendations for vibration prediction and dynamic attenuation of honeycomb sandwich hemispherical shell structures in aerospace engineering. [ABSTRACT FROM AUTHOR]

• The CFRCs honeycomb sandwich structures are fabricated integrally by 3D printing technique. • The damage types at each stage of the flatwise compression process of 3D printed CFRCs honeycomb sandwich structures are successfully characterized. • A 3D printing method for CFRCs honeycomb sandwich structures with multilayer sandwich and core/panel variable printing thickness is proposed. • The compressive strength and energy absorption capacity of multilayer CFRCs honeycomb sandwich structures have obvious advantages. Continuous fiber reinforced composites (CFRCs) 3D printing technology has the advantage of integrated fabricating for honeycomb sandwich structures, the load-bearing capacity of the fabricated honeycomb sandwich structures still needs to be investigated and improved. This study aims to reveal compression failure modes of 3D printed CFRCs honeycomb sandwich structures with various internal configurations by conducting flatwise compression tests. The deviations of single-layer CFRCs honeycomb cores with different core sizes and core heights and their impacts on the compression failure process were analyzed. A 3D printing method with multilayer cores and core/panel variable printing thickness was proposed, and the effects of multilayer core structure and different core printing parameters on the compressive properties of honeycomb sandwich structures were investigated. The results showed that interlayer cracking caused by core buckling deformation was the leading cause of failure of 3D printed CFRCs honeycomb sandwich structures when subjected to compression. The core buckling deformation could be suppressed by printing multilayer cores and using low core printing thickness, and the compression strength and specific energy absorption of the sandwich structures reached 38.1 MPa and 25.4 kJ/kg, respectively. This study provides guidance for the customization of the 3D printing process of CFRCs honeycomb sandwich structures. [Display omitted] [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 presence of serrated ligaments in the re-entrant auxetic honeycomb (abbreviated as serrated RAH) effectively enhances the stiffness while maintaining auxeticity in the re-entrant direction. To investigate its auxetic characteristics, a 3D equivalent Cauchy model (3D-ECM) was established using the variational asymptotic method. The unique aspect is that the engineering constants are obtained by homogenizing the representative unit-cell and then utilized in the 3D-ECM for global analysis. Subsequently, the resulting global responses are fed into the recovery relationships for localized field analysis. The accuracy of the 3D-ECM and the recovered local field distributions were confirmed by comparing them with the results obtained from the three-dimensional FE model (3D-FEM) and the experimental data collected from the 3D-printed specimen. The effects of the geometric parameters on the negative Poisson's ratio and engineering constants were in-depth discussed. Specifically, an optimal value of 0.5 for the re-entrant ratio and d-value (corresponding to the re-entrant angle of 90 degree) yield maximum auxeticity and comparatively higher elastic moduli. In addition, the 3D-ECM greatly enhanced the computational efficiency without compromising the accuracy in predicting global behaviors and local field distributions. The unit-cell tailorability in the proposed model offers valuable guidance for optimizing the design of serrated RAHs. • The presence of serrated ligaments enhance stiffness while maintaining auxeticity. • Engineering constants are obtained by homogenizing the unit-cell within 3D-ECM. • Auxeticity of the serrated RAH is investigated using a VAM-based 3D-ECM. • The accuracy of the 3D-ECM is validated against 3D-FEM and experimental data. • A re-entrant angle of 90-degree yield maximum auxeticity and higher elastic moduli. [ABSTRACT FROM AUTHOR]

• Energy absorption of MRHC on two in-plane principal directions is comparable. • The MRHC are theoretically, experimentally and numerically studied. • More pronounced NPR effect can be attained by implementing misplaced design. • MRHC possesses in-plane bidirectional excellent two plateau stresses. Reinforced honeycomb exhibits exceptional energy dissipation capability. A misplaced design was introduced into reinforced honeycomb (RHC) in this paper, and a novel misplaced reinforced honeycomb structure was proposed (MRHC). The in-plane mechanical properties of MRHC was investigated experimentally, numerically and theoretically. MRHC possesses two plateau stresses in the two in-plane principle directions during low-velocity impact, while the RHC structure demonstrates this characteristic solely in one in-plane direction. The collapse modes and energy absorption performance of the MRHC structure under various impact velocities were investigated. The plateau stress behavior of the MRHC structure was investigated under various unit rotation angles. The two plateau stresses of the MRHC structure exhibit higher values when compared to the previously proposed structure with two plateau stresses. The structures exhibiting two-stage deformation characteristics can determine the extent of collision damage by analyzing the transformation of their structural configuration, establishing a foundation for the design of intelligent structures. [ABSTRACT FROM AUTHOR]

• A corner-enhanced biomimetic spider web hierarchical structure was designed. • Bio-inspired spiderweb honeycomb structures can effectively enhance energy absorption efficiency and achieve rapid energy dissipation. • Bio-inspired spiderweb honeycomb structures corner enhancement and graded enhancement mechanisms are revealed. • The effects of helix radius ratio and radial thickness on the specific energy absorption of honeycomb were investigated. To improve the energy absorption properties of honeycomb structures based on the underlying mechanism of uniform stress dispersion and to effectively increase the strength of a spiderweb, a corner-enhanced spiderweb hierarchical honeycomb structure was proposed herein. This study involved a quasistatic compression test and simulation of a corner-enhanced spiderweb hierarchical structure complemented by 3D printing. The deformation pattern of the common spiderweb honeycomb (CSH) was //-shaped. However, the deformation pattern of the honeycomb after corner enhancement tended to be monolithic, forming an X shape. The deformation characteristics of both the CSH and the first-order local cellular elements were analyzed. The corner-enhanced honeycomb cellular elements dispersed the load onto the inner wall to achieve a common load-bearing effect. Further numerical simulation analysis was carried out in conjunction with the experiments, and local destruction analysis was performed for single-cell elements. Corner enhancement could increase the plastic hinge energy absorption of the structure, with a first-order corner-enhanced spiderweb honeycomb (CESH-F) exhibiting a 46.3 % improvement in specific energy absorption compared to that of a conventional CSH. The layers were reinforced to compress the load uniformly, and a third-order corner-enhanced spiderweb honeycomb (CESH-T) had a 25.7 % improvement in specific energy absorption compared to that of the CESH-F. In addition, optimization was performed for corner-enhanced spiderweb honeycomb (CESH) according to different helix radii. The effect of the radial line thickness on honeycomb-specific energy absorption was explored, and the radial line thickness was positively proportional to honeycomb-specific energy absorption. These findings offered valuable insights into the design of lightweight and high-energy-absorbing biomimetic structures. [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]

• A novel light-weight and high load-bearing C/C honeycomb structure was fabricated. • The accurate model of honeycomb structure containing void defects is established. • A multi-scale damage model for C/C honeycomb structure is developed. • Effects of weave modes and defects on mechanical and failure features are given. The combination of honeycomb structure and carbon/carbon (C/C) composites offers unique high load-bearing and light-weight advantages in satellite-bearing platforms. However, the defects generated by the imperfect preparation process are inevitable. This paper employs the chemical vapor infiltration (CVI) technique to fabricate novel C/C honeycomb structures and considers the presence of internal void defects. Based on micro-computerized tomography (μ-CT) images, the void distribution and porosity as well as the micro-structure characteristics are acquired. Meso-scale representative volume element (RVE) models is established to predict the performance of honeycomb wall material. A secondary development of ABAQUS is performed to establish a model of honeycomb structure containing void defects. Multi-scale models are developed for investigating the mechanical performance of the C/C honeycomb structure. Experimental methods and finite element simulations are utilized to examine the effects of porosity and different weave structures on the compression and shear properties, as well as damage modes of C/C honeycomb structures in detail. The results demonstrate that the presence of low porosity ρ = 1 % severely diminishes the load-bearing capacity of the honeycomb and affects its damage pattern. Twill-2 weave C/C honeycomb inherits the advanced performance of the composites and exhibits superior comprehensive properties compared to plain weave and twill-1 weave honeycomb structures. [ABSTRACT FROM AUTHOR]

• Cuttlebone-inspired honeycomb with asymmetric sinusoidal walls is first proposed. • Effect of the wall amplitude and gradience on the crushing performances are revealed. • The mechanism of honeycomb is fully studied through FEM and the elastic theory. Inspired by cuttlebone microstructure, this study proposes a novel bionic square-tube cuttlebone-inspired honeycomb (S-CIH) structure prepared by digital light processing (DLP) method. Fifteen configurations of honeycombs of same mass including S-CIH, regular honeycomb (S-RH) and sinusoidal honeycomb (S-SH) structures are evaluated and compared in terms of the deformation behavior and compressive performances under out-of-plane compression, especially energy-absorbing capacity. The results indicate that the S-CIH structure achieves the improved energy absorption 8.859 J/g, over 40 % and 60 % than that of S-RH and S-SH structure with same relative density and mass, respectively. The mechanism analysis of the asymmetric corrugated walls disposed in cross and parallel in S-CIH, reveals that the magnitude of amplitude determines the buckling mode thus folding mode of walls, and the magnitude of amplitude gradient determines whether the whole honeycomb structure can achieve a progressive failure. Optimal structural ratio can enable S-CIH delay the complete failure and improve the long-term failure-resistance. This indicates that S-CIH design has the potential ability to strengthen and toughen other brittle matrix materials, and the cuttlebone-like architecture provides a new biological design of mechanically efficient meta-honeycomb beyond conventional honeycomb structure. [Display omitted] [ABSTRACT FROM AUTHOR]

• Introduced an optimized and expanded three dimensional steady-state transition structure. • Proposed a novel impact-resistant structure based on the steady-state transition design. • Demonstrated significant energy absorption features and energy oscillations in the steady-state transition structure under impact. • Highlighted the development potential of steady-state transition structures in the field of impact resistance. Advancements in materials science and mechanical system have spurred widespread investigation into non-traditional structures. In particular, engineers have shown interest in steady-state transition structures with phase transition properties. In this paper, a three-dimensional steady-state transition structure was established using the genetic algorithm and three-dimensional expansion, on which the low-velocity impact tests were carried out. Force response and energy absorption of the steady-state transition structures under impact were studied. From the force response and energy absorption curves, it can be seen that the steady-state transition structures absorb and store portion of impact energy temporarily, gradually releasing it after impact peak. This unique energy behavior results in a steady state transition structure with a long impact response time and a low peak impact force under impact. In addition, investigation into energy transfer within these structures reveals that energy oscillations occur among multilayered bistable surfaces during steady-state transitions, further improving the energy dissipation. Further, the dynamic response and damage modes of the honeycomb structure and the steady state transition structure were compared, showing that the damage mode of the steady state transition structure under the impact is an overall damage, in contrast to the penetration damage of the honeycomb structure. Notably, the steady-state transition structures showcase a higher proportion of elastic strain energy during impacts, effectively delaying structural damage onset, and dispersing impact energy, thus enhancing impact resistance. In light of these findings, the demonstrated behavior of steady-state transition structures in absorbing and dissipating impact energy showcases their potential as promising avenues for the development of more effective impact protection strategies. [ABSTRACT FROM AUTHOR]

• Size-dependent behaviors of auxetic honeycomb sandwich nanoplates is developed. • The proposed approach utilizes a nonlocal strain-gradient isogeometric analysis which incorporates the effects of both nonlocality and strain gradient. • The sandwich nanoplate consists of a core layer featuring an auxetic honeycomb and two outer skin layers reinforced with graphene nanoplatelets. • The length scale parameters can high-efficiently predict size effects. • Some novel benchmark numerical results are illustrated and introduced. Honeycomb structures, which are known for being lightweight and stiff, are still being researched and developed. They have been used in a wide range of industries, but their full potential has not yet been realized. In this study, a novel computational approach for exploring the size-dependent behaviors of auxetic honeycomb sandwich nanoplates is developed. The proposed approach employs a nonlocal strain-gradient isogeometric analysis integrating the influences of nonlocality and strain gradient into the nanoplate structures. The sandwich nanoplate consists of a core layer featuring an auxetic honeycomb with a negative Poisson's ratio, complemented by two outer skin layers reinforced with graphene nanoplatelets (GNPs). This configuration not only achieves exceptional lightweight characteristics through the utilization of auxetic honeycomb cells but also enhances structural stiffness by incorporating GNPs into the skin layers. The material properties of the core layer are determined using cellular cell formulas, while the reinforcement of the two outer skin layers with GNPs is calculated using the modified Halpin-Tsai model. Numerous numerical examples are conducted to investigate the influence of various parameters on the frequencies of the auxetic honeycomb sandwich nanoplates. Notably, the geometrical dimensions of the auxetic honeycomb cells and the nonlocal and length scale parameters emerge as significant influencers on the results. As the first analysis of honeycomb structures at small dimensions, our findings stand as valuable benchmarks for future analyses. [ABSTRACT FROM AUTHOR]

• Hybrid hierarchical square honeycombs (HHSHs) with different configurations were fabricated and tested for evaluating their in-plane elastic modulus. • 11 machine learning (ML) models are trained using a database with 234 results from experimentally validated FE models. • A modified theory for the in-plane elastic modulus of HHSH is developed based on the XGBoost model and existing theory. • The upper and lower bounds of the in-plane elastic modulus of HHSH are determined by the modified theory. • Based on the SHAP method, a quantitative comparison of the importance of hierarchical parameters is conducted. In this study, experimental, finite element (FE) simulation, machine learning (ML), and theoretical techniques are employed to investigate the in-plane elastic modulus (E HHSH) of hybrid hierarchical square honeycombs (HHSHs). First, HHSHs with different configurations were fabricated using a 3D printer, and in-plane quasi-static compression tests were conducted on them. Then, 234 FE models are simulated to determine the E HHSH of HHSHs with various configurations, and the results are used to train 11 ML models. Comparative analysis demonstrates that the Extreme Gradient Boosting (XGBoost) model has the best predictive capability. Moreover, a modified theory for E HHSH is established based on the XGBoost model and existing theory, and its exceptional predictive capability is verified by comparing with experimental, FE, and existing theoretical results. Finally, the upper and lower bounds of E HHSH are determined by the modified theory, and the Shapley Additive Explanation (SHAP) method is used to identify the importance of different geometric parameters on tailoring E HHSH. The combination of theoretical and ML techniques provides a promising approach for developing a robust prediction model of material properties. [Display omitted] [ABSTRACT FROM AUTHOR]

• A new non-uniform rectangular honeycomb sandwich panel is designed based on Bezier curves to enhance material utilization. • The effective elastic constants of non-periodic honeycombs are obtained through the geometric equivalent method and the strain energy-based homogenization method. • The analytical solutions of bending and buckling responses of the non-uniform rectangular honeycomb sandwich panel are derived by using parabolic shear deformation theory. • The weight/performance multi-objective optimization design of the non-uniform rectangular honeycomb sandwich panel is conducted. Honeycomb sandwich panels have a wide range of applications in aerospace, marine and energy industry due to their high stiffness-to-weight ratio. In this study, a new non-uniform rectangular honeycomb core is presented to promote its material utilization ratio. The non-uniform wall of honeycomb core is described using Bezier curves, and the effective elastic constants are obtained by both the geometric equivalent method and the strain energy-based homogenization method. To analyze the bending and buckling behaviors of the sandwich panel, the parabolic shear deformation theory is adopted, and the governing equations are derived by employing Hamilton's principle. Then, the closed-form solutions of bending and buckling responses of the non-uniform rectangular honeycomb sandwich panel are derived. Furthermore, multi-objective design formulations are established, with the objectives of minimizing the weight and deflection, and maximizing the critical buckling load. Illustrative examples demonstrate that the non-uniform design of the honeycomb core can remarkably increase the material utilization rate and improve the mechanical performance of sandwich panels. [ABSTRACT FROM AUTHOR]

• A bistable structure was proposed by introducing cosine-shaped beams. • Configuration and geometric parameter can modulate the ν of the structure. • The structural tunable vibration isolation property was verified by experiments and simulations. With the increasing demand for vibration-isolation structures with tunable and multifunctional properties driven by the rapid development of complex engineering applications, metamaterials have emerged as promising candidates for this purpose owing to their extraordinary properties derived from their unique structural configurations. Owing to their unique deformation mechanisms, negative Poisson's ratio structures have been extensively studied in terms of vibration isolation and energy absorption; however, research on their performance tunability remains lacking. This paper describes a bistable honeycomb mechanical metamaterial (BHMM) consisting of cosine-shaped beams, which exhibits transformable Poisson's ratio and tunable vibration isolation properties. The proposed structure exhibited bistable properties, i.e., undergoing a configuration transition under external forces and retaining its existing configuration after the loading was removed. Furthermore, the two stable configurations exhibited distinctive elastic vibration characteristics, allowing the manipulation of elastic wave propagation on a subwavelength scale via local resonant mechanisms. Overall, this study presents a design methodology for multi-performance tunable metamaterials that satisfy the demands of the external environment. For example, the tunable vibration-isolation property of metamaterial makes it intriguing safety protection structures during crash events. [ABSTRACT FROM AUTHOR]

• 2.5D woven carbon-fiber honeycomb sandwich structures was manufactured and investigated both experimentally and numerically. • Effects of varied parameters of the sandwich structure on the mechanical, especially the energy absorption characteristic were investigated through quasi-static indentation experiments. • The panel strength and honeycomb core strength were found synergistically determine the failure mode of the sandwich structure. Here, a new type of sandwich structure made of fiber metal laminates (FMLs) as facesheet and 2.5D woven carbon-fiber (CFRP) honeycomb as core was developed. The FMLs/CFRP honeycomb sandwich structures were subjected to quasi-static indentation tests to investigate the mechanical response with the variation of panel structure, honeycomb cell element size, honeycomb core wall thickness, and honeycomb core height. In addition to experiments, a finite element method (FEM) model was also created in ABAQUS/Explicit to analyze the damage mechanisms and failure modes of honeycomb sandwich structures under quasi-static indentation. Both the experimental and FEM simulation results revealed that the honeycomb sandwich structure underwent two different failure modes under quasi-static loading: localized damage dominated by indentation and global damage due to overall bending deformation. The combination of panel strength and honeycomb core strength determined the failure mode of the sandwich structure. Damage analysis of the honeycomb core showed that it mainly underwent fiber compression damage and matrix compression damage under quasi-static indentation. This study provides guidance to optimize the design of honeycomb sandwich structures. [ABSTRACT FROM AUTHOR]

In recent years, origami honeycomb metamaterials have garnered extensive attention from researchers. Re-entrant origami honeycomb metamaterials exhibit excellent mechanical performances by virtue of lightweight, high-energy-absorbing characteristics and diverse configurations. In this study, the gradient re-entrant origami honeycomb metamaterials are designed by changing significant geometric parameters. To investigate the effects of geometric parameters variations on compressive behaviors, the theoretical analysis model of the re-entrant origami honeycomb is built to predict the compression stress under low-velocity and high-velocity impact. Subsequently, the energy absorption of the uniform re-entrant origami honeycomb (UROH), the gradient-thickness re-entrant origami honeycombs (GTROHs) and the gradient-angle re-entrant origami honeycomb (GAROHs)are investigated under different compression velocities. The impact resistances of UROH, GTROHs and GAROHs are discussed systematically. By adjusting the gradient distribution of thickness, the deformation modes and Poisson's ratio curves of the structure could be altered. Furthermore, under the high-velocity impact, the specific energy absorption (SEA) of the unidirectionally negative GTROH is increased by 36% than that of UROH at the strain of 0.29. The SEA of the unidirectionally positive GTROH is higher by 14.4% than that of UROH at the strain of 0.8. In addition, the unidirectionally positive GTROH exhibits better impact resistance performance than UROH by comparing the peak stress and SEA value under different compression velocities. This study is expected to provide the new route for designing advanced origami-inspired honeycomb structures and improving buffer protection devices. • Gradient re-entrant origami honeycombs are proposed by varying significant parameter of cells. • An analytical model is established to estimate the plateau stress of the present structure. • Deformation modes and energy absorption of gradient origami honeycombs are investigated. • The crashworthiness of uniform and gradient re-entrant origami honeycombs are discussed. [ABSTRACT FROM AUTHOR]

• The mechanical behavior of carbon fiber reinforced polymer honeycomb cores under in-plane and out-of-plane quasi-compression loads was explored. • Digital image correlation was used to obtain full-field strain evolution and distribution of plastic hinges during compressive loading. • In out-of-plane compression, the cores underwent progressive failure, forming a plastic hinge line. • In transverse direction compression, the cores produced continuous diagonal shear bands. • In ribbon direction compression, diagonal shear band first appeared in the cores, followed by layer-by-layer crushing. In order to meet the urgent demand for the application of composite honeycomb sandwich structures, Carbon fiber reinforced polymer (CFRP) honeycomb cores were made by the hot press molding method. The mechanical behavior of the honeycomb cores under in-plane and out-of-plane compression loadings was explored, including deformation process, energy absorption mechanism, and damage modes. The research focused on the correlation between macroscopic response and local deformation, as well as the influence of loading direction on the deformation process. Digital image correlation (DIC) was used to obtain full-field strain evolution and distribution of plastic hinges during compressive loading. Especially, 2D-DIC was established to obtain the full-field strain distribution of the front and side of the cores during in-plane compression. The experimental results showed that progressive failure of the cores occurred under out-of-plane compression. The deformation was dominated by the bending deformation and the compressive deformation of cell walls when compressed in the W and L directions, corresponding to diagonal shear and layer-by-layer failure, respectively. In addition, the failure mechanism was identified by optical microscope and scanning electron microscope (SEM). This study provided a better understanding of the compressive response of the CFRP honeycomb structures. [ABSTRACT FROM AUTHOR]

• Honeycomb sandwich structures with continuous density gradients are designed. • Flexural behavior is sensitive to horizontal but insensitive to vertical gradients. • Achieved favorable flexural resistance with horizontal arched density distribution. • Detrimental effects from thin cover plates and honeycomb layers are indicated. Sandwich structures with graded cellular cores exhibit promising flexural performances, but their reliance on gradient continuity and distribution warrants further exploration. In this study, seven honeycomb sandwich structures with diverse continuous density gradients, encompassing horizontal, uniform and vertical variations, were designed based on the Voronoi technique and fabricated via 3D printing. Quasi-static three-point bending tests and numerical simulations were conducted to comprehensively analyze the flexural response of density-graded honeycomb sandwich structures. The results reveal a significant influence of the honeycomb core's density distribution on flexural performance, with pronounced sensitivity to horizontal distribution (perpendicular to the loading direction) and less sensitivity to vertical distribution. A favorable flexural resistance is achieved by strategically assigning higher relative density cells to the mid-span of a honeycomb core layer, gradually diminishing towards the ends, which was further optimized into an arched density distribution along the horizontal direction. The influences of cover plate and honeycomb thicknesses on the deformation mechanisms and energy absorption were also investigated, and indicate that thin cover plates and honeycomb layer have a detrimental effect on the bending load-bearing and energy absorption of the sandwich structure. [ABSTRACT FROM AUTHOR]

• A novel origami honeycomb acoustic metastructure is proposed as an effective impact energy absorber. • The metastructure features superior low-frequency sound and impact energy absorption capacities. • The origami foldcore and the top panel are the key components in absorbing impact energy. • Energy absorption efficiency of the metastructure can be enhanced by tuning its geometric parameters. The ancient art of origami has inspired the design and fabrication of numerous acoustic and energy-absorption mechanical metamaterials and metastructures. This study introduces an origami-inspired honeycomb acoustic metastructure designed for engineering applications that demand both high impact resistance and effective sound absorption. This acoustic metastructure is formed by bonding a panel containing periodically distributed perforated holes and a panel without perforations to a periodical array of trapezoidal origami-bellow units. Acoustic wave propagation and drop-weight impact simulations are conducted to investigate the acoustic performance and low-velocity impact behavior of the metastructure. The results show that the origami-bellow honeycomb structure exhibits superior sound absorption capacity over two frequency ranges, outperforming the conventional honeycomb-core sandwich structure. Furthermore, it is shown that, in comparison with both the conventional hexagonal honeycomb-core and the Miura-ori foldcore sandwich structures, the proposed acoustic metastructure demonstrates higher levels of impact resistance and energy absorption capacity. We also show that the mechanical performance of the introduced metastructure under low-velocity impact loads can be further enhanced by increasing the story height of the origami-bellow units. Besides, the matrix material of the origami foldcore can be tailored to suit various scenarios, providing noise control and collision robustness for a diverse range of engineering applications. [Display omitted] [ABSTRACT FROM AUTHOR]

• The deformation behaviors of aluminum honeycomb sandwich panels with artificial defects of different sizes under in-panel compression were investigated using mirror-assisted MV-DIC. • Dual-surface in-plane deformation fields and through-thickness strain fields were measured. • The honeycomb sandwich panel exhibits local undulations and strain concentrations in the surface with defects. • Only defects with sufficiently large sizes leads to decreases in the buckling load. • The bending direction of the buckled specimen is influenced by the local undulations caused by the defect. Honeycomb sandwich panels have been extensively utilized in the aerospace and automotive industries for their prominent advantages of energy absorption, high strength and tailorable anisotropic mechanical properties. Nevertheless, the common presence of local core-to-skin disbonding poses an urgent need to understand the mechanical behaviors of defective honeycomb sandwich panels. The present work investigates the deformation behaviors and evolutions of aluminum honeycomb sandwich panels with varying sizes of circular artificial core-to-skin disbonding defects using mirror-assisted multi-view digital image correlation (MV-DIC). Based on the 3D profiles and dual-surface deformation fields obtained with mirror-assisted MV-DIC, it is revealed that disbonding defects induced local surface undulations with severe local strain concentrations and determined the mode of gradual bending and buckling. Defects with a diameter below 20 mm induced minor local surface undulations and slight decreases in buckling load. When the diameters of defects reach 30 mm, extensive surface convex deformation occurs and the buckling load decreases by 23 %. The results validate mirror-assisted MV-DIC as a cost-effective and practical technique for characterizing dual-surface 3D deformation of sheet composite materials and structures. [ABSTRACT FROM AUTHOR]

• A core stagger layered strategy is proposed for the honeycomb sandwich panels. • Experiments indicate availability of the strategy and accuracy of the numerical simulation. • For a given mass and geometrical size, the increase of layer number and cell size consolidate this effect. • The strategy provides a well choice to improve protective capacity of sandwich panels under air blast loading. Metallic honeycomb sandwich panels have been widely used in energy dissipation due to large plastic deformation under impact/blast loading. In this paper, the dynamic response of a honeycomb sandwich panel with stagger-layered core under intensive near-field air blast loading is investigated. Comparative experiments are conducted for stagger-layered and typical honeycomb sandwich panels with the same geometrical size and mass. Numerical simulation has been undertaken based on the experiments. Numerical results coincide well with experimental results on the deformation/failure modes and center-point deflection of back face sheet. The influence of layer number as well as the geometrical parameters on the energy absorption ability of sandwich panels is clarified. Results show that stagger-layer arrangement of honeycomb core greatly improves energy dissipation capability of sandwich panels compared to typical one with the same mass. The increase of layer number and cell size benefits this effect. These findings indicates that core stagger-layer arrangement is a well choice to improve energy dissipation ability of sandwich panels under air blast loading, especially for highly intensive near-field blast loading. [ABSTRACT FROM AUTHOR]

• Out-of-plane stress-strain response of a sandwich panel differs from that of cellular core. • Adhesive height determines densification initiation strain. • Method correctly characterizes densification region, accounts for adhesive effect. • Significant energy absorbed in the densification region for panels with adhesive. • Larger fillets reduced the overall absorbed energy due to lower densification initiation strains. Lightweight aluminum honeycomb sandwich panels are widely used in industrial engineering, particularly in aircraft applications. Due to their thin-walled nature, the honeycomb cell walls are especially susceptible to buckling under out-of-plane compressive loading, while the adhesive fillet that secures the honeycomb to the face-sheet remains intact. This paper investigates the effect of the adhesive geometry and bonding constraints on the out-of-plane compressive response through experimental, Finite Element (FE), and mathematical methods. A hybrid method accounting for adhesive bonding between the face-sheet and the cell walls, and different adhesive fillet geometries was proposed to predict strain onset and stress-strain relationships during densification. The resulting stress-strain curves predicted the energy absorbed by the panels to within 3.5 % of the experimental results. The widely used material model for honeycomb core does not account for densification and underpredicted the absorbed energy by 15.6 %. These findings emphasize the need for detailed adhesive analysis in the design of lightweight, thin-walled sandwich structures. [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]

• A novel composite auxetic reentrant honeycomb structure is designed and fabricated. • The underwater impact properties of composite reentrant honeycomb structure were explored and analyzed by experiment and finite element analysis. • The effect of gradient form, peak pressure and decaying time on the fluid-structure interaction was analyzed and revealed. • The effect of cavitation of composite reentrant honeycomb structure was analyzed and investigated. In this paper, the effects of the gradient form, peak pressure and decaying time on the fluid-structure interaction of composite auxetic re-entrant honeycomb structures was experimentally and numerically investigated. The specimens for this experiment were manufactured by hot-press molding method. The acrylic transparent tube was utilized to accommodate water medium, pistons and specimen during experiment. The exponential decaying shock wave was simulated by accelerating the fly plate to impact the piston based on the one-stage light gas gun system. The incident velocity of the fly plate and process of the fluid-structure interaction response were monitored by high frame rate camera. In addition, the velocity of the shock wave in water was measured by transducers installed at different measuring points. The voltage signal of the dynamic overpressure collected by transducers was amplified by the charge amplifier and recorded by the oscilloscope. On the other hand, finite element software Abaqus/Explicit was applied to simulate the cavitation process of water domain and dynamic response of specimens. The experimental results and numerical results were in good agreement. The results indicated that the increase of the thickness of the fly plate had a certain effect on the propagation velocity of the shock wave, and the increase of the peak pressure would make the cavitation generation position close to the fluid-structure interface and make the cavitation duration longer. And the average structure which has a minimum transformation of 8.12 mm shows better underwater impact resistance than the gradient structure. [ABSTRACT FROM AUTHOR]

• A novel re-entrant double-arrow auxetic honeycomb was proposed. • Three typical deformation modes under different impact velocities were revealed. • Theoretical models of single-plateau and double-plateau stresses were established. • The effects of impact velocity and geometric parameters were explored. A novel re-entrant double-arrow honeycomb (RDAH) has been proposed and investigated by combining re-entrant hexagonal honeycomb and double-arrow honeycomb. Quasi-static compression experiments of 3D printed samples in different loading directions were carried out. Deformation modes and stress–strain response have been explored and identified. The corresponding finite element (FE) models were established and verified, and the dynamic crushing behaviors of RDAH were further investigated by FE simulations. The results show that RDAH has three typical deformation modes under different impact velocities. When subjected to quasi-static loading and low-velocity impact along the horizontal wall, two stress plateau regions of the stress–strain curves can be observed, while there is only one stress plateau when loaded perpendicular to the horizontal wall. Based on deformation modes, theoretical models of plateau stresses of RDAH under low-velocity and high-velocity impact were further established. The theoretical results of the plateau stresses agree well with the FE simulation results. The effects of impact velocity and geometric parameters on densification strain, Poisson's ratio and energy absorption were also discussed. The results show that the RDAH exhibits obvious negative Poisson's ratio effect in both directions. The energy absorption of RDAH is higher when loaded along the horizontal wall and can be 29.45 % higher than the traditional RH structure. The energy absorption of RDAH increases with the decrease of inclined wall l 1 , the decrease of inclined angle θ (perpendicular the horizontal wall), and the increase of inclined angle θ (along the horizontal wall). [ABSTRACT FROM AUTHOR]