This study systematically investigates the mechanical behavior and equivalent elastic properties of hexagonal honeycomb structures during their topological evolution into quasi-square and re-entrant honeycombs driven by characteristic angles. Based on Euler–Bernoulli beam theory and Timoshenko beam theory, equivalent mechanical models encompassing bending, tensile, and transverse shear effects are established for all three structures, revealing the smooth transition of mechanical properties under continuous variation of characteristic angles and addressing the gap in traditional models that neglect the influence of wall thickness and nodes. Polylactic acid (PLA) specimens were fabricated using fused deposition modeling (FDM) and subjected to uniaxial compression tests, combined with ABAQUS finite element simulations, to validate the accuracy of the theoretical models (average error < 5%). The findings include: (1) As the characteristic angle θ approaches 0°, the hexagonal honeycomb degenerates into a quasi-square structure, and its equivalent elastic modulus can be directly derived from the hexagonal model; when θ evolves negatively, a re-entrant honeycomb is formed, exhibiting a significant negative Poisson’s ratio effect (experimental values: νxy = − 1.537, νyx = −0.618); (2) The wall thickness ratio (l/t) significantly affects mechanical properties, and for <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5695_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">$l/t < 5$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>l</mi> <mo stretchy="false">/</mo> <mi>t</mi> <mo><</mo> <mn>5</mn> </mrow> </math></EquationSource> </InlineEquation>, the Timoshenko theory provides more accurate predictions than the Euler–Bernoulli theory; (3) The Poisson’s ratio can be precisely controlled through the characteristic angle and the proportion of positive/negative-angle units, offering a theoretical basis for the design of gradient auxetic metamaterials. Through a multi-scale approach (theory–experiment-simulation), this study achieves continuous tunability analysis of the mechanical properties of honeycomb structures, providing critical theoretical and experimental support for the design of lightweight materials, energy absorption devices, and multifunctional metamaterials.

Characteristic topological evolution and mechanical behavior analysis of hexagonal honeycomb

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发表日期：

2025年6月30日

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Xiang Li,
Lei Xiong,
Ningchuang Li,
Junjian Fu,
Linjun Wang

摘要

This study systematically investigates the mechanical behavior and equivalent elastic properties of hexagonal honeycomb structures during their topological evolution into quasi-square and re-entrant honeycombs driven by characteristic angles. Based on Euler–Bernoulli beam theory and Timoshenko beam theory, equivalent mechanical models encompassing bending, tensile, and transverse shear effects are established for all three structures, revealing the smooth transition of mechanical properties under continuous variation of characteristic angles and addressing the gap in traditional models that neglect the influence of wall thickness and nodes. Polylactic acid (PLA) specimens were fabricated using fused deposition modeling (FDM) and subjected to uniaxial compression tests, combined with ABAQUS finite element simulations, to validate the accuracy of the theoretical models (average error < 5%). The findings include: (1) As the characteristic angle θ approaches 0°, the hexagonal honeycomb degenerates into a quasi-square structure, and its equivalent elastic modulus can be directly derived from the hexagonal model; when θ evolves negatively, a re-entrant honeycomb is formed, exhibiting a significant negative Poisson’s ratio effect (experimental values: ν_xy = − 1.537, ν_yx = −0.618); (2) The wall thickness ratio (l/t) significantly affects mechanical properties, and for $l/t < 5$ $l / t < 5$ , the Timoshenko theory provides more accurate predictions than the Euler–Bernoulli theory; (3) The Poisson’s ratio can be precisely controlled through the characteristic angle and the proportion of positive/negative-angle units, offering a theoretical basis for the design of gradient auxetic metamaterials. Through a multi-scale approach (theory–experiment-simulation), this study achieves continuous tunability analysis of the mechanical properties of honeycomb structures, providing critical theoretical and experimental support for the design of lightweight materials, energy absorption devices, and multifunctional metamaterials.