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The low stiffness resulting from substantial core porosity within the re-entrant honeycomb sandwich panel can be addressed by introducing rib-reinforcements. To investigate its static and vibration characteristics, an energy-based 2D equivalent-homogenization model (2D-EHM) was derived through asymptotic analysis of the leading terms in the governing equations considering the energy-related characteristics. The accuracy of the constructed model for predicting the elastic bending performance of the sandwich panel was verified by comparing the results of a three-point bending experiment with 3D-printed specimens. Comparative analysis with a 3D FE model demonstrates that the 2D-EHM exhibits maximum errors of only 4.65% and 6.46%, respectively, in analyzing static deformation and natural frequency while improving computational efficiencies by up to 59- and 173-folds. Parameter analysis reveals that the performance of SP-RRH is minimally affected by the reinforcement-to-honeycomb wall thickness ratio. However, its performance is compromised when the honeycomb walls align in an equilateral triangle with the reinforcing walls. Comparing specific stiffness as well as static and vibration characteristics of sandwich panels with different core configurations (including traditional and diamond reinforced re-entrant honeycombs) shows that inclusion of rib reinforcements enhances deformation resistance and natural frequencies through increased specific stiffness. These findings provide valuable insights for optimizing design of re-entrant honeycomb sandwich panels. [Display omitted] • VAM-based 2D model of SP-RRH accurately validated against 3D-FEM results. • Equivalent stiffness obtained via asymptotic analysis of unit cell's energy functional. • The tailorability of the unit cell facilitates the customization of its properties. • Rib-reinforcing walls enhance deformation resistance of sandwich panels. • The performance of SP-RRH is influenced by equilateral triangular cellular structure. [ABSTRACT FROM AUTHOR]

• Three novel lattices by inserting honeycomb struts into the traditional 3D auxetic structure were proposed. • The tensile and compressive mechanical behaviours of hybrid lattices were studied and compared. • 3D hybrid lattices are more effective in tension-dominated applications. Lattice structures have the potential for application in tensile conditions. However, limited studies have addressed tensile behaviours of such structures and compared them with their compressive behaviours. In this paper, re-entrant structure as the foundation was selected to develop new 3D hybrid auxetic honeycomb lattice structures, each characterized by a unique unit cell configuration that features interconnected centre auxetic honeycomb, differentiating it from 2D hybrid auxetic honeycomb structures. A series of uniaxial quasi-static tensile and compressive tests, followed by simulations were conducted on these structures to investigate and compare their energy absorption characteristics. The results show that there were significant differences between these structures in terms of their mechanical behaviours under tension and compression. Especially, the smallest value of energy absorption under tensile load was 86% higher than the largest value under compressive load. The stiffnesses of these lattice structures under tensile loading were about 84–122 times of those of the identical corresponding structures when they were compressed. Meanwhile, the progressive stretching, buckling and collapse mechanisms observed in these structures exhibited excellent stiffnesses and energy absorptions under tensile and compressive load compared to traditional 3D auxetic as the basic structure. The outer frame structure of lattice structures had a direct influence on Poisson's ratio. The work indicates that the stiffness and energy absorption of the traditional 3D auxetic structure can be enhanced by embedding auxetic and honeycomb umbrella shaped elements. [Display omitted] [ABSTRACT FROM AUTHOR]

This study proposes a novel sandwich panel with an improved star-shaped honeycomb (SP-ISH) by replacing sharp corners with cubic struts and lengthening inclined ribs of traditional honeycomb. To more effectively analyze its special dynamic characteristics, the bending Poisson's ratio was derived and effective engineering constants were obtained through asymptotic analysis of the energy functional stored in periodic unit cells. Based on this analysis, a two-dimensional equivalent downscaling model (2D-EDM) was developed to investigate the free vibration of SP-ISH under various boundary conditions, and the influence of initial deformation on free vibration was also discussed. The frequency-domain and time-domain analyses were employed to identify the resonance characteristics of the SP-ISH under harmonic loading. Our findings demonstrate that 2D-EDM can accurately predict the free and forced vibration of SP-ISH and improve computational efficiency by reducing DOFs. The results indicate that the maximum resonance response was obtained by applying excitation at the center of the sandwich panel. Additionally, under cyclic loading, a sharp change in local stress amplitude was observed in the facesheet-core interface region. Compared with traditional star-shaped honeycomb, the incorporation of extended ribs and added struts could significantly reduce the maximum resonance amplitude by 3.8%. Notably, the natural frequencies of SP-ISH were affected by initial compression (up to a 40.6% reduction) and tensile deformation (up to a 26.4% increase). [Display omitted] • Improved SSH design with added cubic struts and elongated inclined ribs. • VAM-based 2D-EDM is developed for free and forced vibration of SP-ISH. • SP-ISH has superior dynamic characteristics other honeycomb sandwich panels. • Initial deformation from support movement impacts free vibration. • 2D-EDM accurately predicts resonance amplitude for various excitations. [ABSTRACT FROM AUTHOR]

• Novel REAT honeycomb structure derived from bio-inspired gradient-based distribution. • Extensive experiments were conducted to decipher different stages of compression and mechanical properties. • Discovery of a new driver for deformation based on the difference in negative poisson's ratio between layers. • Uncovered 80% higher elastic stiffness and 20% larger densification strain for Chiral-based gradient distribution than its conventional counterpart. • Early-stage compression demonstrated 60% more plateau stress and constant 25% higher energy absorption efficiency. This study focuses on the nature-inspired gradient-based approach to re-designing re-entrant anti-trichiral (REAT) honeycombs through extensive experimental quasi-static compression. Novel perspectives on REAT honeycomb are offered through the introduction of gradient distributions on two critical geometrical parameters, the cylindrical diameter (chiral) and height of the unit cell, rather than the traditional thickness-based gradient approach. Chiral-based gradient approach demonstrated clear advantages in elastic stiffness, specific energy absorption (SEA) and densification strain over uniform REAT structures of constant geometrical parameters. These advantages are exhibited in their extended and constantly increasing quasi-plateau stage, consistent specific energy absorption (SEA) especially during early stages of compression, and most importantly, the ability to maintain a relatively constant energy absorption efficiency that is 25% more than that of the Base uniform REAT structure. Height gradient-based REAT structures, on the other hand, were able to leverage on associations between the negative Poisson's ratio (NPR) effect and height of unit cell to demonstrate notable deformation patterns across various portions of the structure. The present work reveals the performance enhancements through alternative gradient-based approaches over thickness-based gradient approaches and highlighted the differences in NPR between layers as the main driver of compressive collapse apart from the commonly concluded difference in relative density. [Display omitted] [ABSTRACT FROM AUTHOR]

A novel hierarchical re-entrant honeycomb metamaterial is proposed by integrating the re-entrant honeycomb (RH) with square unit cell and named as square re-entrant honeycomb (SRH). The novel hierarchical re-entrant honeycomb can not only improve energy absorption capacity but also present better vibration insulation compared with traditional RH structure. Dynamic crushing behaviors of the SRH structures are investigated theoretically and numerically. The theoretical plateau stress is in good agreement with the numerical plateau stress. Meanwhile, the deformation modes and energy absorption capacity of RH and square re-entrant honeycombs (SRHs) are compared under different impact velocities. The results show that the plateau stress and the specific energy absorption (SEA) of SRHs is higher than RH. Moreover, the vibration isolation capability of the SRHs is studied using finite element analysis. In particular, the introduction of square unit cells expand the band gap, especially in the low frequency range. By adjusting the size of oscillators, the starting and stopping frequencies of band gaps are lower effectively and the number of band gaps is increased. The results indicate that the introduction of the mass inclusions can improve the band gap characteristics of the SRH, which produce local resonance effect and the local resonance type band gap. It also appears multiple band gaps at the same time. In addition, the introduction of the mass inclusions also improves the SEA of the SRH under high-velocity crushing. This work may benefit structural vibration isolation and protection design, which provides a new thought for design and development of advanced multi-functional composite structures and materials in the engineering. [Display omitted] • A novel dual-functional metamaterial is proposed by integrating the re-entrant honeycomb with square unit cells. • The energy absorption capacity of the present metamaterial is investigated theoretically and numerically. • Band structure and vibration transmittance of the present metamaterial with or without local resonant inclusions are considered systematically. • Band gap and energy absorption performance of the present metamaterial with local resonant inclusions are researched. • The novel hierarchical re-entrant honeycomb metamaterial has enhanced energy absorption and excellent vibration insulation. [ABSTRACT FROM AUTHOR]

• Novel bionic cores are proposed, whose unit cell is composed of sinusoidal beams. • Bionic cores improve the crashworthiness and load bearing capacity. • Theoretical model shows the relationship between force and geometric parameters. • The wall thickness, amplitude and number of cells can affect crashworthiness. In this paper, novel bionic sandwich cores are proposed based on the cross section of seagull feather shaft to provide an effective protective mechanism against impact. The relative density of the bionic core is firstly defined, which is closely related to cell configuration and geometric parameters. Through finite element simulations supported by experiments using 3D printed specimens, the novel bionic core is found to be superior in crashworthiness as compared to conventional honeycomb core in terms of specific energy absorption and mean force under out-of-plane compression. To decipher the underlying mechanisms for the enhanced performances, a theoretical model for the bionic core is derived based on the simplified super folding element (SSFE) theory. The effects of wall thickness, number of cells and amplitude of sinusoidal beam on relative density and crashworthiness are explored. It is revealed that the increase in wall thickness and number of cells led to improvements of load bearing capacity. An optimal structure is subsequently obtained based on the complex proportional assessment (COPRAS) and response surface method (RSM). Compared to conventional honeycomb core, the optimal peak force of the bionic core is decreased by 11.53%. Through the combination of experiment, simulation and theoretical analysis, this study provides a novel idea for the optimization of the crashworthiness of the bionic core under out-of-plane compression. [Display omitted] [ABSTRACT FROM AUTHOR]

• A simple re-entrant auxetic metamaterial is designed by rotating and connecting 2D re-entrant honeycomb cells. • The energy absorption of the proposed metamaterial is discussed under different design parameters. • The proposed 3D re-entrant auxetic lattice has desirable stiffness and specific energy absorption. • The initial peak stress and energy absorption capacity of the metamaterial can be adjusted via changing design parameters. As a branch of auxetics, the re-entrant hexagonal honeycomb has many superior mechanical performances. However, most research focused on two-dimensional (2D) re-entrant structures or three-dimensional (3D) structures without high compressibility. The energy absorption capacity of such structures is deficient for practical applications. Therefore, it is important to investigate the 3D re-entrant honeycomb structures which can sustain large deformation in order to make the most use of the materials. In this work, a simple 3D re-entrant unit cell is designed, manufactured and examined. The influence of geometric parameters on the deformation mode and energy absorption capacity is investigated numerically. The experimental results are in good agreement with the finite element prediction. The proposed 3D re-entrant auxetic metamaterial not only possesses a greater bearing capacity but also presents a stable compression deformation. The structure exhibits a desirable energy absorption behavior, including obvious auxetic behavior and a long stress plateau. By adjusting the geometrical parameters of the structure, the performances of energy absorption and compression stiffness can be improved. These findings provide a new idea to design 3D auxetic metamaterials and promote their utilization in protective structures. [Display omitted] [ABSTRACT FROM AUTHOR]

• The representative unit cell (RVE) of CVH is divided into three sub-regions with independent thickness parameters according to the position of the hexagon. • The influence of different thickness distributions on the performance of CVH is investigated to explore the conditions for the emergence of dual-platform features. • Four key design parameters of the whole energy absorption process are extracted, which are derived theoretically based on the stable deformation modes. • A detailed parametric design strategy of the CVH specimen is proposed based on the theoretical analysis, which can regulate the energy absorption curve to the required range. The center-vertex honeycomb (CVH) structure based on the self-similar hierarchical evolution of the hexagonal honeycomb (HH) is introduced in this paper. The CVH structure has stable deformation modes, excellent energy absorption performance, and multi-platform features, and can be applied to multi-stage energy absorption devices with special requirements, such as energy-absorbing components of vehicles and trains. In this study, the multi-stage energy absorption characteristics of CVH under the in-plane quasi-static compression load are investigated numerically and theoretically, which is verified by the experimental test. The representative unit cell (RVE) of CVH is divided into three sub-regions with independent thickness parameters according to the position of the hexagon. The effects of different thickness distributions on the performance of CVH are investigated to explore the conditions for the emergence of dual-platform features. Then, the four key design parameters of the whole energy absorption process are extracted, which are derived theoretically based on the stable deformation modes. Further, a detailed parametric design strategy of the CVH specimen is proposed based on the specific engineering requirements. The design results proved that the proposed design strategy is reliable and accurate, which provides valuable suggestions and guidelines for the regulation of the energy absorption process of relevant structures for specific engineering needs. [Display omitted] [ABSTRACT FROM AUTHOR]

• A correlation between the mesoscale mechanisms, the evolution of the contact and deformation-induced stresses, and the plateau stresses at the impact and support ends is established. • The defect location has higher influence on the energy absorption capacity of a honeycomb than the relative proportion of defects. • The effect of defects on the macroscopic response in a honeycomb diminishes with increase in impact velocity. • The dissipation performance is the highest for honeycombs with defects located close to the support end for impact velocities in the range 75–150 m/s. In this work, we investigate the dynamic compressive response of hexagonal honeycombs with defects in the form of missing cell walls for various impact velocities. Five types of honeycombs have been considered including a defect-free structure. The influence of the defect locations on the deformation bands, the local accelerations, the contact-induced, and the deformation-induced stresses have been discussed. A new parameter, termed as the bias factor, has been introduced to account for the type of the missing cell wall defects. A hexagonal unit cell has two vertical and four inclined cell walls. For a given defect percentage, we vary the relative proportion of the missing inclined and the missing vertical walls through the bias factor. The effect of the relative proportion of defects and the location of defects on the energy absorption capacity and the plateau stresses at the impact and the support ends has been discussed. The simulations reveal that the defect location causes a significant reduction in the energy absorption capacity as compared to the relative proportion of defects. It is observed that the sensitivity of the dynamic performance of the honeycombs to the presence of the defects reduces as the impact velocity increases. We define a non-dimensional dissipation performance parameter β , to evaluate the performance of various honeycomb types. It is found that the honeycombs with defects concentrated at the support end show the highest dissipation performance for impact velocities in the range 75–150 m/s. [ABSTRACT FROM AUTHOR]