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In-Plane Mechanical Behavior Design of a Locally Rib-Reinforced Rotating Hexagonal Honeycomb

Biomimetics 2026, 11(3), 172; https://doi.org/10.3390/biomimetics11030172

by Jialiang Xie¹, Jinjin Huang¹ and Xiaolin Deng^2,*

Reviewer 1: Anonymous

Reviewer 2: Anonymous

Reviewer 3: Anonymous

Biomimetics 2026, 11(3), 172; https://doi.org/10.3390/biomimetics11030172

Submission received: 28 January 2026 / Revised: 17 February 2026 / Accepted: 26 February 2026 / Published: 2 March 2026

(This article belongs to the Section Biomimetics of Materials and Structures)

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript proposes a locally rib-reinforced rotating hexagonal honeycomb (LRRH) by integrating rotationally arranged hexagonal cells with embedded triangular units and internal ribs. Abaqus/Explicit simulations, validated by quasi-static compression tests, are used to study in-plane axial crushing. By varying re-entrant angles and introducing symmetric hybrid assemblies, the work evaluates deformation modes, stress–strain response, Poisson’s ratio, and specific energy absorption (SEA). The results show distinct angle-dependent behavior, identify high-performing two types of configuration, and indicate greater wall thickness and higher impact velocity markedly increase SEA and modify crushing mechanisms. Some revisions should address the following concerns before publication:

(a) Given that the manuscript’s core focus is the Locally Rib-Reinforced Rotating Hexagonal Honeycomb (LRRH), it is recommended that the Abstract and Conclusions be revised so that between-group comparisons (e.g., LRRH vs. RRH and other relevant baselines) are highlighted more prominently than within-group comparisons, thereby allowing the design rationale of LRRH and its mechanical advantages to be presented more clearly. (see: Golden-Ratio–Guided Aperiodic Architected Metamaterials with Simultaneously Enhanced Strength and Toughness, Advanced Functional Materials, 2025)
(b) It is recommended to improve the readability of the figures. In addition, the figures should explicitly illustrate the design origin and evolution of the proposed LRRH and clearly distinguish the key geometric features of RRH versus LRRH.
(c) The experiments are conducted using PLA specimens, whereas the simulations adopt AA6061-O as the base material. The authors are encouraged to clarify this discrepancy and provide a clear justification for why the numerical material model is not consistent with the experimental material, and how this choice affects the validity and scope of the conclusions.
(d) All abbreviations should be explicitly defined at their first occurrence in the Abstract and again in the main text where appropriate. Symbols should not be reused in a way that introduces ambiguity (b in Eq. (1) and Fig. 4). For example, ‘LRRH’ and the parameters in Fig. 4 (a1–a5, b1–b5¬) should be clearly defined. In addition, vt in Eq. (3) should be explicitly defined.
(e) It is suggested to clearly specify how the densification strain is defined and determined
(f) Based on Figs. 16 and 22, the LRRH appears to exhibit lower SEA and mean stress than the RRH in several cases. The authors are encouraged to clarify where the advantages of LRRH lie, and to articulate the corresponding scientific significance to avoid confusion regarding the motivation for introducing LRRH.
(g) The manuscript should be thoroughly revised for the English language, grammar, tense, and overall clarity.

Author Response

Given that the manuscript’s core focus is the Locally Rib-Reinforced Rotating Hexagonal Honeycomb (LRRH), it is recommended that the Abstract and Conclusions be revised so that between-group comparisons (e.g., LRRH vs. RRH and other relevant baselines) are highlighted more prominently than within-group comparisons, thereby allowing the design rationale of LRRH and its mechanical advantages to be presented more clearly. (see: Golden-Ratio–Guided Aperiodic Architected Metamaterials with Simultaneously Enhanced Strength and Toughness, Advanced Functional Materials, 2025)

RE: We are very grateful for the reviewer's valuable comments. We entirely agree that a comparative analysis between structural groups can more intuitively demonstrate the original design intent and the superiority of mechanical performance. Following your suggestion, we have performed targeted and in-depth revisions to the Abstract and Conclusion sections, and have incorporated the relevant references in appropriate places.

(b) It is recommended to improve the readability of the figures. In addition, the figures should explicitly illustrate the design origin and evolution of the proposed LRRH and clearly distinguish the key geometric features of RRH versus LRRH.

RE: We appreciate the reviewer’s valuable suggestions. We fully agree that enhancing the readability of figures and clearly presenting the evolution of the structural design are crucial for improving the overall clarity of the manuscript. In the revised version, a schematic diagram of the structural design evolution has been added to intuitively demonstrate the origin and evolutionary process of the proposed LRRH structure.

(c) The experiments are conducted using PLA specimens, whereas the simulations adopt AA6061-O as the base material. The authors are encouraged to clarify this discrepancy and provide a clear justification for why the numerical material model is not consistent with the experimental material, and how this choice affects the validity and scope of the conclusions.

RE:Thank you for the reviewer’s valuable comments. Regarding the inconsistency between the materials used in the experiments and those in the finite element model, our primary consideration was to verify the accuracy of the numerical model through comparison with the experimental results, thereby providing a reliable basis for subsequent model development. The deformation patterns obtained from the experiments and simulations show a high degree of consistency, and the energy absorption error remains within 5%, demonstrating that the finite element model can accurately capture the mechanical response of the structure. After completing this validation, aluminum alloy was adopted in the subsequent analyses, mainly because it is widely used in practical collision and impact applications in engineering.

(d) All abbreviations should be explicitly defined at their first occurrence in the Abstract and again in the main text where appropriate. Symbols should not be reused in a way that introduces ambiguity (b in Eq. (1) and Fig. 4). For example, ‘LRRH’ and the parameters in Fig. 4 (a1–a5, b1–b5¬) should be clearly defined. In addition, vt in Eq. (3) should be explicitly defined.

RE: We thank the reviewer for the meticulous review and valuable suggestions. We have conducted a comprehensive check and standardization of all abbreviations and symbols throughout the manuscript. In the revised version, the formulas and symbols have been clarified and modified as requested, with these changes clearly reflected in the updated text.

(e) It is suggested to clearly specify how the densification strain is defined and determined.

RE: We thank the reviewer for the valuable comments. Regarding the ambiguity of certain parameter definitions, we have added a detailed description of the identification method for the densification stage in Section 4 (Mean Stress Analysis) of the revised manuscript. The basis for determining densification strain and its calculation method have been clarified, followed by a brief explanation of its role in evaluating energy absorption performance.

(f) Based on Figs. 16 and 22, the LRRH appears to exhibit lower SEA and mean stress than the RRH in several cases. The authors are encouraged to clarify where the advantages of LRRH lie, and to articulate the corresponding scientific significance to avoid confusion regarding the motivation for introducing LRRH.

RE: We appreciate the reviewer’s insightful comments. The design motivation for the LRRH is not merely to pursue an absolute increase in SEA across all parameters. Its core scientific significance lies in the strategic introduction of local stiffeners at the vertices of the rotating hexagons to creatively construct parallelogram support units. This aims to systematically explore the fundamental differences in load transfer and deformation coordination mechanisms between these units and the triangular units in the original structure.Although the SEA of the LRRH is slightly lower than that of the RRH in certain configurations, our study reveals that the introduction of parallelogram units significantly enhances the performance growth potential under specific geometric constraints (e.g., small internal angles). Furthermore, it effectively mitigates stress concentration at the nodes, providing a more stable and controllable deformation mode and positive Poisson's ratio characteristics compared to the RRH. Accordingly, a detailed comparative analysis has been added to Section 4.1 of the revised manuscript.

(g) The manuscript should be thoroughly revised for the English language, grammar, tense, and overall clarity.

RE: We thank the reviewer for the valuable suggestions. We have conducted a comprehensive revision and polishing of the English language throughout the manuscript. Specific focus was placed on correcting grammatical errors, addressing inconsistent tense usage, and clarifying ambiguous expressions to enhance the overall logic and readability of the paper.

Reviewer 2 Report

Comments and Suggestions for Authors

Overall, the deduction of this manuscript is correct, and the results of this manuscript are believable. I think this manuscript could be published in Biomimetics after major revisions that will be listed as following:

1 The experimental work is a key part of the manuscript, but the "Finite Element Analysis Model Validation" section is critically lacking in detail. The authors state they fabricated samples and performed tensile and compression tests but provide almost no information on the procedures. For example: Dimensions of the honeycomb compression specimens, and images of the test setup, and details of the testing machine, loading rates, and data acquisition.

2 The validation section is confusing. The manuscript stated that "local fractures in the early stage of compression" were observed experimentally, but the simulation "does not account for material fracture behavior." But the authors conclude the model has "high reliability." In additions, Fig. 9 compared experiment and simulation, showing significant deviation in the post-yield region, yet this is glossed over. A more critical discussion of the discrepancies between experiment and simulation and the limitations of the FEM model are required.

3 The discussion sections are long blocks of text that are very difficult to read. The interpretations are often superficial and descriptive. The manuscript fails to explain the underlying mechanics of why one structure performs better than another.

4 The manuscript calculated and plotted the dynamic Poisson's ratio in Fig. 15. However, the discussion of this result is extremely limited. It simply states that one curve is positive and the other shows negative values. There is no attempt to explain the complex, strain-dependent evolution of the Poisson's ratio or link it to the observed de formation modes.

5 The references in the introduction are inadequate. To increase the readership of current paper, some recent studies on nonlinear dynamic responses or coupled physical fields should be added to enrich research background. For example: Journal of Applied Mechanics, 2023, 90(9): 091008; International Journal of Mechanical Sciences, 2024, 270: 109091.

6 The physical and mechanical meanings are not specifically mentioned in the discussion. The authors should analyze specific reasons in revised manuscript.

7 The grammatical and spelling errors should be carefully considered in the revision.

Author Response

This study investigated the improved mechanical performance and energy absorption of forced rotating hexagonal honeycombs under in-plane impact. The research combined experimental quasi-static compression tests on 3D-printed samples with dynamic finite element simulations in Abaqus/Explicit. It evaluates the dynamic response and energy absorption characteristics against a more conventional re-entrant hexagonal counterpart, considering the effect of varying re-entrant angles.Overall, the deduction of this manuscript is correct, and the results of this manuscript are believable. I think this manuscript could be published in Biomimetics after major revisions that will be listed as following:RE：

RE: We thank the reviewer for the valuable comments. We agree that the descriptions of the finite element model validation and experimental procedures in the original manuscript were not sufficiently centralized or comprehensive, which may have impacted the reproducibility and clarity of the study. To address this, the geometric dimensions and structural parameters of the honeycomb compression specimens have been clearly specified in Section 3.1. The compression test setup and loading schematic are now provided in Figure 6. Furthermore, we have refined the testing procedures, key experimental details, and image acquisition methods for both compression and tensile tests in Section 3.3.

RE: We appreciate the reviewer's professional comments and agree that the discrepancies between the experimental and numerical results require further clarification. In the physical experiments, certain manufacturing defects existed in the connection areas of the honeycomb specimens due to the inherent limitations of 3D printing precision. Additionally, the intrinsic brittleness of the PLA material led to localized fracture phenomena at various stages of the compressive loading. These factors collectively contributed to the observed deviations between the experimental results and numerical simulations during the post-yield stage.Nevertheless, multiple sets of repeated compression tests demonstrated that the overall trend of the stress–strain curves remains highly consistent, with the error in total energy absorption between the simulation and experiments controlled within 8.8%. Based on the comprehensive comparison of global deformation modes, initial response stages, and energy absorption levels, we believe the current finite element model reasonably reflects the macroscopic mechanical response of the structure. This also confirms the rationality and reliability of the established model in terms of boundary conditions, load application, and overall modeling methodology.

RE: We thank the reviewer for the valuable comments. We agree with the assessment that the Discussion section in the original manuscript was overly lengthy, lacked sufficient readability, and required a deeper mechanistic analysis. Accordingly, we have restructured the Discussion into three distinct subsections: (1) Deformation modes of RRH, (2) Deformation modes of LRRH, and (3) Crashworthiness comparison.Within these sections, we have strengthened the comparative analysis between the structures. To further elucidate the performance discrepancies, we have provided supplementary explanations regarding deformation mode evolution, load transfer paths, and local mechanical responses. Furthermore, a more in-depth discussion on the deformation behavior and energy absorption mechanisms during critical mechanical stages has been incorporated.

RE: We thank the reviewer for the valuable comments. We agree that the discussion regarding the dynamic Poisson's ratio results was insufficient. The analysis of Fig. 15 in the original manuscript primarily remained at the descriptive level, without fully elucidating the complex evolution of the Poisson's ratio with strain and its intrinsic correlation with structural deformation modes. To address this issue, we have supplemented and deepened the relevant content in Section 4.1 of the revised manuscript. We further analyzed the evolutionary characteristics of the Poisson's ratio at different strain stages and discussed the underlying mechanisms behind the transition from positive to negative values (or sustained negative values) in conjunction with the key deformation stages during compression.

RE：We sincerely thank the reviewer for the valuable suggestion. We fully agree that the Introduction section previously lacked sufficient references and that the research background required further elaboration. In the revised manuscript, the Introduction has been substantially expanded and improved.Following the reviewer’s recommendation, we have incorporated several recent studies related to nonlinear dynamic response and multiphysics coupling behavior, including representative works published in Journal of Applied Mechanics (2023, 90(9): 091008) and International Journal of Mechanical Sciences (2024, 270: 109091), among others.In addition, we have strengthened the review of recent research progress and clarified the connection between these studies and the present work. These revisions enhance the completeness, timeliness, and relevance of the research background.

6 The physical and mechanical meanings are not specifically mentioned in the discussion. The authors should analyze specific reasons in revised manuscript.

RE：We sincerely thank the reviewer for the valuable comment. In response to the concern that the physical significance and mechanical implications were not sufficiently clarified, we have strengthened and expanded the discussion of the underlying structural response mechanisms in the revised manuscript.Specifically, a more systematic and in-depth interpretation has been provided by correlating unit geometric characteristics, load transfer paths, local buckling behavior, and deformation mode evolution. Through this comprehensive analysis, the differences in structural performance and their corresponding formation mechanisms are now more clearly explained. The relevant revisions have been incorporated and highlighted in the corresponding sections of the manuscript.

7 The grammatical and spelling errors should be carefully considered in the revision.

RE:We sincerely appreciate the reviewer’s careful reading and constructive suggestion. The manuscript has undergone a thorough and comprehensive language revision. Grammatical errors, spelling issues, and unclear expressions have been systematically corrected, and several sentences have been refined to improve clarity, accuracy, and overall readability. All corresponding revisions have been fully incorporated into the revised manuscript.

Reviewer 3 Report

Comments and Suggestions for Authors

This manuscript proposes a new honeycomb topology to improve energy absorption under compression. The authors use Abaqus to simulate the mechanical responses of honeycomb structures and compare the results with experiments. They also compare the responses for honeycombs with different geometric parameters. The overall research is systematic, and the manuscript is generally well-written. However, the manuscript could be improved by addressing the following detailed comments before publication.

In the Abstract, the abbreviation “RRH” seems undefined. What is the difference between LRRH and RRH?
In the Introduction, the authors claim that “the geometric connections between adjacent units are optimized.” The authors could comment on how optimization is achieved. Do they use any optimizers?
In Section 3.3, the authors mention that “… were fabricated using a RAISE 3D Pro Plus 3D printer, employing polylactic acid (PLA) as the printing material.” What is the infill pattern used for 3D printing, and how do authors account for the infill-pattern-induced and printing-direction-induced material anisotropy?
8 shows that the honeycomb structures experienced large deformations. The authors could detail how the material and geometrical nonlinearity are modeled in their Abaqus simulation. Do they use a hyperelastic model? Which model (e.g., neo-Hookean) is used?
9 shows that, compared to FEA, the experimental honeycomb structures exhibit higher energy absorption. However, the FEA does not account for brittle fracture and should lead to stronger structures and greater energy dissipation. The authors could comment on this counterintuitive point.
Contact simulation is important for the accurate simulation of structures under compression. The authors could use a simple example to introduce how the contact model works in their simulations.
It would be helpful to compare the performance between the proposed and classical honeycomb topologies, instead of only comparing the performance of the proposed honeycombs with different parameters.
In Section 6, the authors claim that “these findings provide a viable and effective strategy for optimizing the energy-absorbing performance of honeycomb structures.” It deserves a more detailed explanation.

Author Response

1.In the Abstract, the abbreviation “RRH” seems undefined. What is the difference between LRRH and RRH?

RE:We sincerely thank the reviewer for the careful review and valuable comments. We have revised the abstract by providing the full definition of “RRH” at its first occurrence, and we have also clarified it again at its first mention in the main text. Moreover, to avoid potential confusion for readers, the distinction between LRRH and RRH has been further clarified in the revised manuscript.

2.In the Introduction, the authors claim that “the geometric connections between adjacent units are optimized.” The authors could comment on how optimization is achieved. Do they use any optimizers?

RE：We sincerely thank the reviewer for the professional and insightful suggestion. The optimization described in this study is primarily reflected in the design of the rotational rigid configuration and the rib-reinforcement scheme. By systematically comparing different connection configurations in terms of load transfer paths, local deformation modes, and overall mechanical performance, the structural layout was screened and refined to identify a more advantageous geometric connection scheme.It should be clarified that the optimization process in this work is based on configurational design and comparative mechanical response analysis, rather than on the implementation of an independent numerical optimization algorithm.

In Section 3.3, the authors mention that “… were fabricated using a RAISE 3D Pro Plus 3D printer, employing polylactic acid (PLA) as the printing material.” What is the infill pattern used for 3D printing, and how do authors account for the infill-pattern-induced and printing-direction-induced material anisotropy?

RE:We sincerely thank the reviewer for the valuable comment. The RRH structure specimens were fabricated using laser-based fused deposition modeling (FDM) additive manufacturing.Regarding the concern about material anisotropy, we carefully reviewed relevant literature and confirmed that PLA materials produced under additive manufacturing conditions indeed exhibit a certain degree of anisotropy. Representative studies supporting this observation include: International Journal of Mechanical Sciences (2024, 109223), Composites Communications (2025, 102428), and other related works (DOIs: 10.1007/s43452-024-00895-9; 10.1007/s11433-023-2311-3).To mitigate the influence of printing-induced anisotropy, the printing orientation was strictly controlled during specimen preparation. Specifically, both the tensile specimens and the honeycomb structure specimens were fabricated using the same printing direction. This measure was intended to minimize experimental discrepancies caused by anisotropy and to ensure the comparability and consistency of the experimental data.

4.8 shows that the honeycomb structures experienced large deformations. The authors could detail how the material and geometrical nonlinearity are modeled in their Abaqus simulation. Do they use a hyperelastic model? Which model (e.g., neo-Hookean) is used?

RE: We sincerely thank the reviewer for the valuable comment. An elastic–plastic constitutive model was adopted in the finite element (FE) simulations to accurately capture the nonlinear deformation behavior and plastic buckling mechanisms of the structure under compressive loading.Specifically, during the initial small-deformation stage, the material response is dominated by linear elasticity. When the equivalent stress reaches the yield strength and the structure enters the large-deformation regime, the elastic–plastic constitutive model is activated to characterize the progressive folding, plastic hinge formation, and energy absorption process. This modeling strategy enables a realistic representation of the collapse evolution and load-bearing response of the structure.Furthermore, we have reviewed and referenced relevant studies on similar thin-walled and energy-absorbing configurations (e.g., International Journal of Mechanical Sciences, 2024, 109223), where elastic–plastic material models were likewise employed to describe large-deformation compressive behavior. These references further substantiate the validity and appropripriateness of the adopted modeling approach.

5.9 shows that, compared to FEA, the experimental honeycomb structures exhibit higher energy absorption. However, the FEA does not account for brittle fracture and should lead to stronger structures and greater energy dissipation. The authors could comment on this counterintuitive point.

RE：We sincerely thank the reviewer for the professional and insightful comment. We agree that further clarification regarding the discrepancies between the experimental and numerical results is necessary.In the experimental tests, due to the inherent limitations of 3D printing accuracy, minor manufacturing imperfections were inevitably present in certain connection regions of the honeycomb specimens. In addition, PLA exhibits a certain degree of brittleness, which may lead to intermittent local fracture during compressive loading. These factors collectively contribute to the observed deviations between the experimental results and the numerical simulations, particularly in the post-yield stage.Nevertheless, repeated compression tests demonstrate good consistency in the overall evolution trend of the stress–strain curves. Moreover, the discrepancy between simulation and experiment in terms of total energy absorption is controlled within 8.8%. Considering the agreement in global deformation modes, initial response characteristics, and overall energy absorption levels, the developed finite element model is capable of reasonably capturing the macroscopic mechanical response of the structure. These results further validate the rationality and reliability of the adopted boundary conditions, loading schemes, and overall modeling strategy.

Contact simulation is important for the accurate simulation of structures under compression. The authors could use a simple example to introduce how the contact model works in their simulations.

RE：We sincerely thank the reviewer for the valuable comment. To prevent mutual penetration between the honeycomb structure and the rigid plates during loading, a surface-to-surface contact formulation was defined between the honeycomb specimen and the upper and lower rigid plates. An automatic single-surface contact algorithm was employed to ensure robust contact detection throughout the deformation process.Regarding the contact properties, the tangential behavior was modeled using the Coulomb friction law with a friction coefficient of 0.2. For the normal behavior, a general contact algorithm was adopted to ensure numerical stability and reliability during the contact computation.These contact settings effectively prevent interpenetration and allow for accurate simulation of the interaction between the honeycomb structure and the rigid loading plates.

It would be helpful to compare the performance between the proposed and classical honeycomb topologies, instead of only comparing the performance of the proposed honeycombs with different parameters.

RE：We sincerely thank the reviewer for the valuable suggestion. We agree that including additional comparative analyses could further strengthen the persuasiveness of the results. Considering the scope of this study, which primarily focuses on the configuration design and performance evaluation of the LRRH honeycomb structure, no additional large-scale comparative experiments with conventional honeycomb structures were conducted in this revision.To address the reviewer’s comment, we have supplemented the Discussion section with a systematic comparison among different groups of structures. The comparison covers deformation modes, load-bearing responses, and energy absorption characteristics, providing a more comprehensive and logically coherent analysis of the results.

In Section 6, the authors claim that “these findings provide a viable and effective strategy for optimizing the energy-absorbing performance of honeycomb structures.” It deserves a more detailed explanation.

RE：We sincerely thank the reviewer for the valuable comment. We agree that the optimization strategies discussed in Section 6 require further explanation and support, which has been added in the revised manuscript. Specifically, by introducing a rotationally rigid unit configuration combined with rib-reinforcement design, the internal load transfer paths and local constraint conditions of the structure were effectively regulated. This approach promotes a more stable progressive folding deformation during compression, delays local instabilities, and enhances both the platform-stage load-bearing stability and overall energy absorption efficiency.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have addressed all of my comments.

Author Response

We sincerely appreciate the reviewer’s positive comments and recognition of our work. The encouraging feedback is greatly appreciated.

Reviewer 2 Report

Comments and Suggestions for Authors

The quality of this work has been significantly improved after revision. However, there are still some small issues that need to be pay attention to:

1 Refs. [48, 49] were mentioned in the main text, but not given in reference list.

2 There are still some grammar and typo errors. Please further check the manuscript and improve the manuscript.

Author Response

1 Refs. [48, 49] were mentioned in the main text, but not given in reference list.

RE：We sincerely thank the reviewer for the valuable suggestion. According to the reviewer’s recommendation, References 48 and 49 have been added to the revised manuscript to further strengthen the literature support of this study.

2 There are still some grammar and typo errors. Please further check the manuscript and improve the manuscript.

RE：We sincerely thank the reviewer for the valuable comment. The manuscript has been thoroughly revised and carefully edited to improve the overall English language quality. Grammatical errors and unclear expressions have been corrected, and the clarity and readability of the manuscript have been significantly enhanced.

Author Response File: Author Response.pdf

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In-Plane Mechanical Behavior Design of a Locally Rib-Reinforced Rotating Hexagonal Honeycomb

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