Re-entrant Honeycomb Research Articles

Phase Diagrams for Anticlastic and Synclastic Bending Curvatures of Hexagonal and Re-entrant Honeycombs

Abstract Transformation between saddle- and dome-like bending shapes of regular and re-entrant hexagonal honeycomb panels are explored. An analytical model is proposed to uncover the underlying mechanisms and identify the controlling parameter when the cell walls are slender beams. Then, 3D finite element simulations are performed to examine the architecture dependence of bending shape and construct the phase diagrams of anticlastic and synclastic curvatures when the cell walls have a general geometry. The results are believed helpful to the design and application of related honeycomb structures.

Energy absorption characteristics and auxetic effect of novel elliptic-arc re-entrant honeycomb structures

The novel elliptical-arc re-entrant honeycomb (ERH) is designed by substituting the straight inclined struts within the re-entrant honeycomb with elliptical-arc struts. To assess its performance effectively, the study established the 3D equivalent Cauchy model (3D-ECM) and 2D equivalent Kirchhoff–Love model (2D-EKM) using the variational asymptotic method. The equivalent properties derived from the unit-cell constitutive model were integrated into the equivalent models for macroscopic analysis. Through 3D printing experiments and numerical simulations, the model’s accuracy in predicting the compression behaviors and auxetic effects of various uni- and multi-cellular ERHs under uniaxial compression, as well as the three-point bending behaviors of ERH panels were confirmed. In addition, this model substantially simplifies the modeling process, leading to a 8-fold increase in computational efficiency. Parametric analyses demonstrated that the ERH structure can uphold a beneficial auxetic effect while achieving lightweight and high strength characteristics when the axial ratio of the ellipse equals 1.25. Furthermore, ERH structures outperform arc-shaped re-entrant and regular re-entrant honeycombs in energy absorption and specific energy absorption capacity. These findings offer valuable insights for the preliminary design and optimization of ERH structures.

A comprehensive study on numerical homogenization of re-entrant honeycomb lattice and analytical model assessment

A comprehensive study on numerical homogenization of re-entrant honeycomb lattice and analytical model assessment

Parameter-Independent Deformation Behaviour of Diagonally Reinforced Doubly Re-Entrant Honeycomb.

In this study, a novel unit cell design is proposed, which eliminates the buckling tendency of the auxetic honeycomb. The novel unit cell design is a more balanced, diagonally reinforced doubly re-entrant auxetic honeycomb structure (x-reinforced auxetic honeycomb for short). We investigated and compared this novel unit cell design against a wide parameter range. Compression tests were carried out on specimens 3D-printed with a special, unique, flexible but tough resin mixture. The results showed that the additional, centrally pronounced reinforcements resulted in increased deformation stability; parameter-independent, non-buckling deformation behaviour is achieved; however, the novel structure is no longer auxetic. Mechanical properties, such as compression resistance and energy absorption capability, also increased significantly-An almost four times increase can be observed. In contrast to the deformation behaviour (which became predictable and constant), the mechanical properties can be precisely adjusted for the desired application. This novel structure was also investigated in a highly accurate, validated finite element environment, which showed that critical stress values are formed in well-supported regions, meaning that critical failure is unlikely. Our novel lattice unit cell design elevated the auxetic honeycomb to the realm of modern, high performance and widely applicable lattice structures.

Flexural behaviors of asymmetric Re-entrant auxetic honeycombs

A family of negative Poisson's ratio honeycombs with asymmetric base units and potential applications in civil and marine industries are introduced by introducing asymmetricities to the geometry of regular re-entrant unit cell. These structures, namely the single symmetry-broken re-entrant (SSR), double symmetry-broken re-entrant (DSR), and hybrid symmetry-broken re-entrant (HSR) honeycomb lattices, are fabricated through fused filament fabrication and subjected to experimental three-point bending (TPB) experiments and simulations. The novel designs showcase exceptional specific energy absorption (SEA) attributes compared to the regular metamaterial, with the SSR structure exhibiting a remarkable 147.2% higher SEA. The asymmetric metamaterials also demonstrate higher flexural modulus (Ef) compared to the benchmark design, with the SSR and DSR models boasting approximately 29% and 19% higher Ef, respectively. Studies on design parameters show that internal angle of unit cells that creates the asymmetricity affects the flexural performance of the unique auxetic honeycombs, significantly. Finally, parametric investigation on out-of-plane bending of the honeycombs showed the dominance of all asymmetric-unit honeycombs over the benchmark due to having organized self-contact regions. The SSR and DSR structures own about 51% and 39% higher SEA than the benchmark honeycomb under out-of-plane TPB, respectively.

Bending response and energy absorption of sandwich beams with combined reinforced auxetic honeycomb core

This study introduces a reinforced star-shaped auxetic honeycomb (RSSAH) sandwich beam, enhanced with hollow thin-walled tubes to improve bending resistance and energy absorption performance. The bending performance of the RSSAH is systematically investigated through quasi-static three-point bending tests and finite element numerical simulations. The findings suggest that when subjected to mid-span stress, the RSSAH displays both localized indentation and overall bending deformation, accompanied by notable negative Poisson’s ratio (NPR) impact under bending loads. Parametric studies are undertaken by numerical simulations to investigate the impact of compression position, auxetic angle, and face sheet thickness on the bending mode of the auxetic honeycomb sandwich beam. The analysis shows that the RSSAH can exhibit excellent bending performance and, at one of the compression positions, displays double-plateau stress characteristics. It is also found that altering key geometric parameters, such as the auxetic angle and panel thickness ratio, can greatly improve the bending capabilities of the RSSAH, achieving stable plastic deformation and high energy absorption. Finally, compared to star-triangle honeycomb (STH) sandwich beam, traditional reentrant honeycomb (RH) sandwich beam and star-shaped auxetic honeycomb (SSAH) sandwich beam, the RSSAH demonstrates superior bending performance and energy absorption capacity. This study offers insights and references for the development of innovative reinforced auxetic honeycomb sandwich beams.

Automated detection of deformation mechanisms in re-entrant honeycomb auxetics using machine learning

The intricate geometrical configuration of an auxetic structure enables high energy dissipation capacity at the expense of a highly nonlinear mechanical response. Under external stimuli, complicated deformation mechanisms emerge which dictate the extent of energy dissipation. Recently, the new ‘plastic hinge tracing’ method (Dhari et al., 2021) was introduced to detect such deformation mechanisms for elastoplastic porous materials. This approach is however subjective and cumbersome since it requires monitoring several plastic regions in consecutive deformed configurations. The present study innovatively extends this method by implementing machine learning (ML) techniques for objective detection of deformation modes in auxetics. To this end, a logistic regression ML model was developed to classify the deformation modes of a re-entrant honeycomb structure. The proposed procedure could successfully detect four out of the six deformation modes (‘X’, distorted ‘X’, ‘V’, and ‘V + Z + V’) using the training datasets generated by the finite element analysis and image labels created by K-means clustering algorithm. The success of the proposed automated approach lays the foundation for identifying the deformation mechanisms of other auxetics and porous materials with plastic deformations.

Assessing design-induced elasticity of 3D printed auxetic scaffolds for tissue engineering applications

Auxetic scaffolds fabricated via additive manufacturing can enable cyclic mechanical stimulation to promote the biomechanical functionalization of engineered tissues. Typical designs of additively manufactured scaffolds used in tissue engineering literature (e.g., 0/90˚ strand laydown) are not amenable to cyclic loading due to their rigidity, which is in part due to the high stiffness of biopolymers such as polycaprolactone (PCL). Auxetic scaffolds can help overcome this due to their design-induced elasticity while recapitulating negative Poisson’s ratios seen in various natural tissues. In this study, we investigated the effects of auxetic design patterns and unit cell sizes on the mechanical properties of 3D bioplotted PCL scaffolds. First, we assessed the monotonic tensile properties of two auxetic patterns – re-entrant honeycomb and missing rib (unit cell = 3 × 3 mm2 for both) – in comparison to a uniaxial control (0/0˚ strand laydown) using finite element analysis (FEA) and experimental design (n = 3/group). The results showed that the scaffold design significantly impacted scaffold elasticity (p < 0.05), with the missing rib auxetic design demonstrating significantly higher yield strain (48.2 %) compared to the re-entrant honeycomb design (11.0 %) and the control (4.8 %). The missing rib design also possessed significantly lower elastic modulus and tensile strength (11.5 MPa/g and 10 MPa/g, respectively) compared to the re-entrant honeycomb (58 MPa/g and 35.7 MPa/g, respectively) (p < 0.05). For the missing rib design, we further investigated the effect of unit cell size (2 × 2, 3 × 2, 3 × 3 mm2) on the mechanical properties. Both 3 × 2 and 3 × 3 mm2 unit cell scaffolds (n = 3/group) possessed similar mechanical properties whereas the 2 × 2 mm2 unit cell scaffolds possessed significantly lower yield strain and higher elastic modulus and tensile strength (p < 0.05). The missing rib auxetic scaffolds were also tested under tensile cyclic loading for up to 6000 cycles at 10 % of maximum strain at 0.5 Hz. The 2 × 2 mm2 unit cell scaffolds degraded significantly faster than the other two groups. Overall, the 3 × 2 mm2 unit cell scaffolds performed better under cyclic loading in terms of maintaining their tensile strength. Finally, biocompatibility testing of the missing rib 3 × 2 mm2 unit cell scaffolds demonstrated their ability to support the adhesion and viability of fibroblast cells. In future, this knowledge will be leveraged to engineer scaffolds for connective tissues such as tendons and cardiac muscle.

Investigation on the energy absorption characteristics of novel graded auxetic re-entrant honeycombs

In this work, innovative graded auxetic re-entrant honeycombs constructed by adjusting the geometric parameters of a core unit cell are proposed, and their deformation modes and energy absorption characteristics with different impact speeds are systematically investigated. The novel graded design utilizes structural hierarchy on the meso-scale and functional gradient on the macro-scale. The numerical simulation models are verified by comparing the experimental results. The results show that compared with the ungraded honeycomb (URH), one of the graded honeycombs (GRHs), named GRH1, can greatly improve the specific energy absorption by 36.4%, 10.8%, and 6.00% for the quasi-static, low, and high-speed impact at a strain of 0.6. At the same time, the initial peak stress of GRH1 is decreased by 43.2% and 27.1% compared with that of URH for low and high-speed impact, respectively. It could be indicated that the GRH1 was an ideal energy-absorbing structure. This work provides a new route for designing graded auxetic honeycombs with enough insight to understand the deformation mechanism of the structures, which could be used in lightweight buffer protective systems.

Dynamic crushing responses of enhanced auxetic re-entrant honeycomb based on additive manufacturing

Recently, auxetic re-entrant honeycombs have gained a significant deal of attention due to their superior mechanical qualities. In this work, a star-enhanced auxetic re-entrant honeycomb (S-ARH) is proposed by combining a star-shaped re-entrant honeycomb (SRH) with an auxetic re-entrant honeycomb (ARH). Experimentally validated finite element models are used to investigate the deformation modes, horizontal shrinkage strains, and stress-response relationships of the S-ARH at various crushing velocities. The deformation modes of S-ARH are essentially identical to the ARH. The integration of star-shaped structures causes S-ARH to form a compact zone earlier but with a lower horizontal shrinkage capacity. Additionally, the plateau crushing stress σp and specific energy absorption of S-ARH are also calculated to illustrate the ability to absorb energy and the resistance to impact. A methodical equation for the dynamic compressive strength is derived based on the collapse mechanism of the S-ARH, and the finite element confirms the applicability of the derived equation. Finally, an evaluation is conducted to examine how various structural parameters influence the dynamic performance of S-ARH.

Low-velocity impact response of sandwich plates with corrugation star-shaped honeycomb hybrid core

Compared with traditional lightweight corrugation and honeycomb cores, the novel cellular structure exhibiting a negative Poisson's ratio possesses distinctive mechanical deformation features, making it suitable for modeling lightweight sandwich structures. Therefore, the concept of combining the auxetic honeycomb core with folded corrugations is proposed to construct a new type of corrugation star-shaped honeycomb (SSH) hybrid core for studying the dynamic behavior of sandwich panels subjected to low-velocity impact. Integrate Hertz elasticity theory and first-order shear deformation theory (FSDT) to develop an equivalent analytical model, and derive the equations of motion through Hamilton principle. To model contact force interactions during dynamic processes, a spring-mass model is utilized. Analytical solutions are derived for predicting transverse displacement with Duhamel's principle and Navier's method. Numerical simulations are conducted using the Abaqus commercial software, and the validity of the results is confirmed by comparing them with findings in the existing literature. Based on this, effective strategies for enhancing the sandwich panel's resistance to low-velocity impacts are proposed by examining the influence of different side length ratios, thickness ratios, and cell concave angles. In comparison to the corrugation re-entrant hexagonal honeycomb hybrid core sandwich panel structure, the corrugation SSH hybrid core sandwich panel structure reduces transverse displacement by 33.6 % at the same impact velocity.

Study on the energy absorption effect and impact resistance of a composite sandwich panel with carbon fiber reinforced re-entrant hexagonal honeycomb core with negative Poisson's ratio

Negative Poisson's ratio (NPR) structures have excellent energy absorption and buffering properties, but they generally have disadvantage of low specific strength, which restricts their wide applications. Therefore, in this study, the carbon fiber reinforced Nylon material (Nylon 12CF) was prepared and used to construct re-entrant hexagonal honeycomb NPR structure. The reinforced (Nylon 12CF) and unreinforced (Nylon 12) specimens were fabricated by 3D printing technology and tested quasi-statically. Then, the quasi-static of the reinforced and unreinforced re-entrant NPR structure and the impact analysis of the composite sandwich panel (CSP) with re-entrant NPR carbon fiber reinforced core are carried out by finite element method. The results show that the NPR structure reinforced with carbon fiber has 112.5% higher failure stress and 113.9% higher energy absorption efficiency than the unreinforced structure. The finite element simulation results are in good agreement with the experimental results. Under the impact load of a 5 kg object with different initial velocities, the maximum of the displacement of the back face sheet's center point of the CSP with reinforced NPR core is smaller than that of CSP with unreinforced NPR core, especially when the impact velocity is 20 m/s. At different initial impact velocities, the CSP of the reinforced NPR structure core all showed high impact resistance, which was about 1.4 times that of the unreinforced NPR structure core. This research provides new ideas for designing more efficient energy-absorbing and impact-resistant structures.

Analysis of Mechanical Properties and Parameter Dependency of Novel, Doubly Re-Entrant Auxetic Honeycomb Structures.

This study proposes a new, doubly re-entrant auxetic unit-cell design that is based on the widely used auxetic honeycomb structure. Our objective was to develop a structure that preserves and enhances the advantages of the auxetic honeycomb while eliminating all negative aspects. The doubly re-entrant geometry design aims to enhance the mechanical properties, while eliminating the buckling deformation characteristic of the re-entrant deformation mechanism. The effects of the geometric modification are described and evaluated using two parameters, offset and deg. A series of experiments were conducted on a wide range of parameters based on these two parameters. Specimens were printed via the vat photopolymerization process and were subjected to a compression test. Our aim was to investigate the mechanical properties (energy absorption and compressive force) and the deformation behaviour of these specimens in relation to the relevant parameters. The novel geometry achieved the intended properties, outperforming the original auxetic honeycomb structure. Increasing the offset and deg parameters results in increasing the energy absorption capability (up to 767%) and the maximum compressive force (up to 17 times). The right parameter choice eliminates buckling and results in continuous auxetic behaviour. Finally, the parameter dependency of the deformation behaviour was predicted by analytical approximation as well.

Mechanical Properties of Re-Entrant Hybrid Honeycomb Structures for Morphing Wings.

The exceptional energy absorption, deformability, and tuneable Poisson's ratio properties of negative Poisson's ratio (NPR) honeycomb biomimetic structures make them highly suitable for applications in aerospace, medical, and acoustic stealth industries. The present study proposes a re-entrant hybrid honeycomb (REHH) structure comprising a re-entrant octagonal unit cell and a re-entrant hexagonal unit cell. Theoretical models of the in-plane elastic modulus and Poisson's ratio are established based on beam theory, and these models are validated through finite element (FE) simulations and tensile experiments conducted on the REHH samples. The influence of the cell geometry parameters on the in-plane elastic behaviours is investigated. The results indicate that the NPR performance of the REHH structure exhibits superior deformation capability compared with the four-point star hybrid honeycomb (FSHH) structure. The experimental REHH structure samples exhibit significant tensile displacement capabilities in the x-direction.

Inverse design method for tailoring the deflection of beams with functionally graded metamaterials

Abstract Functionally graded metamaterials represent a cutting-edge approach to designing structures with cellular materials. By manipulating parameters in specific regions, a customized mechanical response is achieved, optimizing material utilization. Despite various proposed methods to generate functionally graded structures, the challenge of high computational costs persists. This study introduces a novel and computationally efficient inverse design method for beams featuring segment-wise graded metamaterials. Using a semi-analytical approach based on Castigliano’s second theorem, this method significantly reduces computational demands. The approach leverages prior experimental and computational characterizations of the transverse deflection in rectangular, reentrant, and hexagonal honeycombs. Validation through finite element models and experimental tests on additively manufactured beams confirms the adequate performance of the method. The proposed framework successfully generates beams with targeted deflections, demonstrating the method’s capability for inverse design under specific loading and boundary conditions. This approach not only optimizes material utilization but also broadens the application scope of functionally graded metamaterials in structural design.

Compressive and flexural responses of auxetic sandwich panels with modified re-entrant honeycomb cores

Auxetic structures possess negative Poisson’s ratio (NPR). They exhibit enhanced indentation resistance, synclastic deformation, high fracture toughness and high energy absorption. Several sorts of auxetic structures exist, such as re-entrant, arrowhead, chiral, etc. The re-entrant structure is the most common sort of auxetic structures. This paper investigates the mechanical behavior of the re-entrant auxetic structure using experimental and numerical methods. Two modified re-entrant topologies are proposed based on the original (conventional) re-entrant topology. Using these modified topologies, two re-entrant auxetic sandwich structures are designed and 3D printed using fused deposition modeling (FDM) out of polylactic acid (PLA). Conducting compression, three and four-point bending tests, the compressive and flexural performance of the two new re-entrant auxetic sandwich structures is studied and compared with the original (conventional) re-entrant structure. More specifically, Poisson’s ratio, compressive modulus, flexural stiffness and maximum loads of the structures are focused and studied. The mechanical properties of auxetic sandwich structures are improved using modified topologies. The new re-entrant auxetic sandwich structures show 11% higher normalized compressive modulus and 9% higher normalized flexural stiffness than the original re-entrant structure.

Mechanical properties and prescribed design of a star-shaped re-entrant honeycomb based on multi-objective optimization

Zero Poisson's ratio honeycombs have been widely studied and applied in aerospace and other fields by virtue of their special deformation modes. With the development of intelligence, the optimal design becomes more diversified. In this paper, the mechanical properties of star-shaped re-entrant honeycomb (SRH) are analyzed in the form of parametric modeling, and parameter tuning of SRH is carried out in combination with Latin hypercube sampling. Three options for modifying the response surface model and improving the fitting accuracy are analyzed and proposed. Multi-objective optimization of SRH based on genetic algorithm (NSGA-II) is carried out using the modified response surface model as a proxy model. The SRH is redesigned in the direction of specifying the minimum Poisson's ratio, Young's modulus and mass. The design of the SRH from positive Poisson's ratio to zero Poisson's ratio effect is achieved, resulting in a reduction of Young's modulus by 40.67 % and mass by 42.28 % for the optimal SRH. The application of multi-objective optimal design and response surface modeling correction methods provides new ideas for honeycomb design.

Transient heat transfer analysis of a sandwich panel with a cracked honeycomb core

Sandwich structures with ceramic honeycomb cores are extensively employed in thermal protection systems owing to their exceptional ability to resist high temperatures. This work aims at exploring the effect of cracking on the transient thermal process of the sandwich panel subject to impulsive and cyclic thermal loadings. Both the conventional and re-entrant hexagonal alumina honeycombs are considered for the core material. By the integral transform method, combined with singular integral equations, the transient temperatures of the whole sandwich panel are determined from the semi-analytical solution. The straightforward temperature difference of the crack face’s midpoints is exploited to characterize the heat intensification near the crack. Parametric investigations are carried out for the internal cell angle, the relative density, crack length, crack position, and thickness of face sheets, which provides a better understanding of the honeycomb materials working in thermal protection systems.

A new hybrid auxetic structure capable of uniform deformation exhibits excellent energy absorption

As a kind of mechanical metamaterial, auxetic honeycomb with negative Poisson’s ratio has received extensive attention in recent years. In order to further improve the stable deformation and energy absorption of the auxetic structure, we combined the asymmetrical re-entrant honeycomb with the triangular honeycombs to propose a new two-dimensional (2D) auxetic structure named asymmetrical re-entrant triangular honeycomb (ART). By setting up comparative experiments, quasi-static compression tests for ART and two existing honeycomb structures (re-entrant star-shaped honeycomb and re-entrant hexagonal honeycomb) along in-plane directions were conducted. A series of ART configurations with different parameters were established, and finite element simulation was used to explore the effects of parameters on the mechanical properties of ART. The unilateral horizontal maximum strain is cited to assess the deformation stability of the structures. The experimental and simulation results show that the deformation of ART is uniform in both in-plane directions. In the compressive strain range that we studied, the specific energy absorption of ART in both directions can be up to 291% and 271% higher than that of the existing structures, respectively, providing excellent load-bearing and energy absorption. In addition, the mechanical properties of ART can be adjusted by changing the geometrical parameters to provide ideas for structural design.

Simulation Study on Quasi-Static Compressive Mechanical Properties of Honeycomb Structures with Negative Poisson’s Ratio

Negative Poisson’s ratio structures are widely used in military, aerospace, vehicles, air-dropped packages, and medical devices due to their high strength, stiffness, energy absorption, and impact resistance, but their mechanical properties are significantly affected by geometric parameters. In this paper, for the compression energy-absorbing mechanism of the re-entrant hexagonal honeycomb structure, numerical simulations are used to study the effects of wall thickness and angular gradient on its compression failure mode and energy-absorbing performance. The results show that the wall thickness has little impact on the compression failure mode, while the angular gradient has a significant impact on the compression failure mode. The wall thickness has a significant effect on the energy-absorbing performance, and the larger the wall thickness is, the better the energy-absorbing property is; the energy-absorbing performance of the symmetric negative gradient structure is significantly better than that of the other three angular gradients, and all the four kinds of angular gradient structures have better energy-absorbing performance than that of the conventional re-entrant honeycomb. The results obtained provide a reference for improving the energy absorption performance of negative Poisson’s ratio honeycomb structures under quasi-static compression.