1. Introduction
Bioinspiration is among the most reliable sources of innovation for product design (Reference Domke and FarzanehDomke & Farzaneh, 2018). Through evolution, biological systems have developed ingenious strategies that serve as a foundation for solving modern engineering challenges. Nature-inspired solutions often outperform traditional designs. For example, Lotus (Nelumbo nucifera) leaf-inspired superhydrophobic surfaces (Reference Zhang, Feng, Wang and ZhengZhang et al., 2016), Kingfisher (Ceyx azureus) beak-inspired low puncture force structures (Reference Velivela, Letov, Liu and ZhaoMcKeag, 2012; Reference McKeagVelivela et al., 2021), Honeycomb-inspired energy absorbing structures (Reference Zhang, Yin, Yu and XuZhang et al., 2019), etc. Abstraction of functions exhibited by biological features of over 50 organisms reveals that many biological features serve multiple functions and that analogous functions can arise in different organisms (Velivela & Zhao, Reference Velivela and Zhao2023a). Despite the growing body of work in bio-inspired design, no quantitative parameters have been established to systematically select between the biological features from distant organisms that exhibit identical functionality. The challenge lies in distinguishing which biological feature is best suited for a specific engineering application, as multiple organisms may evolve similar traits to address comparable environmental demands. For instance, it is tough to choose between Shark scales and Dolphin skin that exhibits drag-reducing properties (Reference Yu, Liu, Zhang, Yan, Zhang, Wu, Liu and JiangLuo et al., 2015; Reference Luo, Yuan, Li and WangYu et al., 2020). In nature, this phenomenon is termed as convergent evolution. Convergent evolution refers to the process by which distantly related species independently develop similar biological features, to fulfill equivalent functional roles, such as drag reduction, impact resistance, or water repellence, which are crucial in bio-inspired design for selecting the most relevant biological analogy (Reference Moore and WillmerKasahara, 2010; Reference KasaharaMoore & Willmer, 1997). These traits, recognized as biological adaptations developed by different organisms for similar purposes, pose a unique challenge in early-stage product design, as it involves selecting the most relevant feature from a variety of analogous adaptations. To streamline this selection, designers rely on qualitative parameters, supported by Bio-inspired Design (BID) methods such as BioGEN (Reference Badarnah and KadriBadarnah & Kadri, 2015), System-of-Systems BID (Reference Tan, Sun, Mohan, Brahmananthan, Venkataraman, Sosa and WoodTan et al., 2019), Reduced Function-Means (RF-M) (Reference Bhasin, Adams and LaytonBhasin et al., 2021), and the Trimming method (Reference Zhang, Li, Nie, Yu and LiuZhang et al., 2021). While these methods provide valuable qualitative criteria for identifying suitable biological analogies, quantitative parameters become essential to accurately differentiate traits evolved in similar environments and on comparable scales. To address this issue, quantitative metrics called meta-level design parameters are introduced to facilitate precise selection between biological features with similar characteristics (geometric designation) and functionalities. These parameters were verified through case studies involving impact resistance comparisons of woodpecker’s beak and pomelo peel (Reference Velivela, Letov, Kong and ZhaoVelivela et al., 2023) and drag reduction comparisons of sharkskin and dolphin skin (Reference Velivela, Ridard and ZhaoVelivela et al., 2024). Building on this foundation, this research extends these parameters by introducing novel meta-level design parameters that enable the selection of biological features based on shared functional capabilities, irrespective of geometric similarity. It emphasizes the development of parameters derived solely from the geometry of biological structures, independent of evolutionary influences. A case study of a multifunctional, bio-inspired helmet conceptual design is conducted to investigate the parameter through a comparative study of two different structures that solve the same function. For this study, the impact resistance of the Woodpecker’s beak and Balanus exoskeleton that have the potential to be used as helmet liners are compared.
The paper is organized as follows. Section 2 provides an overview of the Domain Integrated Design (DID) method used for conceptualising the helmet, meta-level design parameters, and influence of geometry in bio-inspired design. Section 3 outlines the conceptual design of the bio-inspired helmet using DID, including geometric modelling and 3D printing of woodpecker beak and Balanus-shaped liners, along with a review of existing bio-inspired helmet liners and impact tests. Section 4 details the experimental and the numerical analysis used for deriving the proposed meta-level design parameters. Section 5 discusses the novel meta-level design parameters, followed by concluding remarks.
2. DID and meta-level design parameters
Domain Integrated Design (DID) categorizes biological features into geometric domains (e.g., Surfaces, Cellular Structures, Shapes and Cross-sections) based on their characteristics. By systematically combining features from different domains, DID enables the development of multifunctional bio-inspired designs across various applications (Velivela & Zhao, Reference Velivela and Zhao2023b). As shown in Figure 1, the bio-inspired helmet integrates features from different doamins, including a penguin’s spindle body shape for drag reduction (Reference Yu, Liu, Zhang, Yan, Zhang, Wu, Liu and JiangYu et al., 2020) – Shape domain, a luffa sponge-inspired structure for effective sweat absorption (Reference Shen, Xie, Huang, Zhou and RuanShen et al., 2012) – Cellular Structure domain, and helmet liners inspired by a woodpecker’s beak (Reference Velivela, Letov, Kong and ZhaoVelivela et al., 2023) – Cellular Structure domain, and Balanus (Reference Ha and LuSan Ha & Lu, 2020) – Shape domain. This study applies the DID method to the conceptual design of a bio-inspired helmet, using it as a means to establish parameters for selecting between morphologically different biological features that perform the same function. Specifically, helmet liners inspired by a woodpecker’s beak and Balanus were designed and evaluated through testing and numerical analysis, demonstrating how DID facilitates systematic decision-making in bio-inspired design.
Conceptual sketch of the helmet liners inspired by woodpecker’s cellular beak and Balanus shape. The helmet shape inspired inspired by a penguin's body for drag reduction and luffa sponge for sweat absorption
2.1. Meta-level design parameters
The meta-level design parameters shown in Table 1 (Reference Velivela, Ridard and ZhaoVelivela et al., 2024) are quantitative parameters that are integrated into the DID method (Reference Velivela and ZhaoVelivela & Zhao, 2022) and the Expandable Domain Integrated Design model (xDID) (Velivela & Zhao, Reference Velivela and Zhao2023b), enabling the selection between biological features exhibiting the same function and belonging to the same Domain (similar geometric relevance). These paramerts were verified through two independent case studies. The first study examines the impact resistance of a non-pneumatic tire inspired by woodpecker beaks and pomelo peels (Cellular Structures Domain) (Reference Velivela, Letov, Kong and ZhaoVelivela et al., 2023). The second study compares drag reduction in swimsuits inspired by sharkskin and dolphin skin (Surfaces Domain), finding sharkskin more effective due to its smaller interaction area (Reference Velivela, Ridard and ZhaoVelivela et al., 2024).
Meta-level design parameters
2.2. Geometric influence in bio-inspired design
In this research, the biological features compared are the woodpecker’s beak classified as the Cellular Structure Domain, and the Balanus-inspired conical structure classified as the Shapes Domain. These features were chosen because they represent distinct geometric adaptations that solve similar functional challenges – impact resistance. By comparing these features, this work aims to illustrate how different geometric strategies can be employed to achieve similar functional goals. As discussed earlier, this research emphasizes the development of parameters based solely on the geometry of biological structures, independent of their evolutionary pressures. For example, the cellular structure of a woodpecker’s beak, adapted for enduring high-frequency repetitive axial loads, offers insights into shock absorption and energy dissipation through its geometry (Reference Lee, Horstemeyer, Seely and WilliamsLee et al., 2013). Conversely, the geometric structure of a barnacle (Balanus) shell, adapted to withstand slower, continuous compressive forces from water pressure and wave impacts, illustrates principles of stability and load resistance (Reference Shaw, Kang, Triano, Hoppe, Aldred, Metzler and DickinsonShaw et al., 2024). While the woodpecker’s beak is designed to prioritize impact deceleration and mitigation, the barnacle’s shell emphasizes structural stability and resilience under compressive forces. However, by focusing on geometry alone, designers can gain insights into the structural benefits that shape can provide under various loading conditions, irrespective of the specific evolutionary stresses that shaped them.
3. Verification of Meta-level design parameters through design, fabrication, and testing
The DID method is employed to generate a multifunctional bio-inspired helmet design. This involves combining biological features, categorized based on their geometric attributes, to achieve diverse functionalities. The resulting helmet integrates a penguin's spindle body shape to enhance drag reduction for the outer body (Reference Yu, Liu, Zhang, Yan, Zhang, Wu, Liu and JiangYu et al., 2020), a luffa sponge-inspired structure for efficient sweat absorption (Reference Shen, Xie, Huang, Zhou and RuanShen et al., 2012), and features inspired by a woodpecker's beak (Reference Velivela, Letov, Kong and ZhaoVelivela et al., 2023) and Balanus (Reference Ha and LuSan Ha & Lu, 2020) for the helmet liners. Geometric modeling of the bio-inspired structures was carried out using LatticeQuery (Reference Letov and ZhaoLetov & Zhao, 2022), a software derived from CadQuery specifically for designing complex cellular structures. This tool was instrumental in accurately replicating the intricate geometries of biological inspirations, such as the gradient porosity of a woodpecker’s beak and the corrugated surface of the Balanus exoskeleton. The gradient porosity characteristic of the woodpecker’s beak, vital for its shock-absorbing capability, was emulated using a lattice structure based on the Schwarz Primitive topology. This design aspect was critical for replicating the beak’s energy absorption efficiency (Reference Letov, Velivela, Sun and ZhaoLetov et al., 2021). The Balanus structure was modeled to include its conical shape and distinctive corrugated surface attributes, that contribute to its resilience against compressive forces. A parametric sinusoidal waveform was utilized to capture the spiral form and corrugations accurately (Reference Letov and ZhaoLetov & Zhao, 2022). These models were fabricated using additive manufacturing, with Formlabs BioMed resin selected for its durability, flexibility, and biocompatibility, ensuring the structural integrity, safety of the helmet liners, and suitability for prolonged skin contact (Reference Ha and LuSan Ha & Lu, 2020).
3.1. Reported bio-inspired helmet liner designs
Bicycle helmet liners draw inspiration from diverse composite and biologically inspired structures, aiming to safeguard the head against rotational accelerations. Ongoing research focuses on integrating bio-inspired designs into helmets, offering significant potential for energy absorption strategies. The outer shell’s key roles include distributing impact loads across a wide area and preventing penetration by sharp objects to avoid skull punctures and brain injuries (Reference Leng, Ruan and TseLeng et al., 2022). The MIPS system, featuring a slip-layer between the outer shell and inner foam, allows sliding to mimic the protective properties of cerebrospinal fluid (Reference Leng, Ruan and TseLeng et al., 2022). Literature explores designs for anti-rotational helmet liners, drawing inspiration from various biological materials and structures, such as coconut material (Cocos nucifera) (Reference Totla, Pillai, Chetan, Warad, Vinodkumar, Patil and KotturshettarTotla et al., 2020), pomelo fruit-inspired structures (Reference Fischer, Thielen, Loprang, Seidel, Fleck, Speck and Bührig-PolaczekFischer et al., 2010), trabeculae bone (Reference Mehta, Ocampo, Tovar and ChaudhariMehta et al., 2016), sheep (Ovis aries) horn-inspired structures (Reference GennarelliGennarelli, 1993), lattice arrays, woodpecker, honeycomb, and conch shell structures (Reference Leng, Ruan and TseLeng et al., 2022).
3.2. Reported study on impact resistance
Various helmet designs were tested for effectiveness in the literature. Examples include oblique impact tests on bicycle helmets using a free-falling head form and a moving sandwich with two aluminium plates, measured with tri-axial quartz force cells (Reference Intosh, Lai and SchilterMcIntosh et al., 2013). Shin-guard structures’ energy absorption was tested under low-velocity impacts using a twin-wire guided vertical impactor (Reference Wang, Chen, Roy and SilberschmidtWang et al., 2023). The BMW Group conducted tensile testing of metal cellular structures (Reference Fischer, Thielen, Loprang, Seidel, Fleck, Speck and Bührig-PolaczekFischer et al., 2010). A recent study compared the effectiveness of pomelo fruit, woodpecker beak, and shell designs using a polycarbonate impactor model in LS-DYNA, revealing that the Pomelo structure exhibited lower deformation than woodpecker and shell designs (Reference Najmon, Jacob, Wood and TovarNajmon et al., 2018).
4. Results
This section is divided into two main subsections that discuss physical experiment results and numerical analysis results, each providing insights into the performance and characteristics of the designed bio-inspired structures under various testing conditions.
4.1. Physical experimentation results
Physical tests were conducted in line with ASTM F1952 standards, employing a 1.6 m drop height to simulate impact conditions relevant to helmet safety (ASTM). The experiments involved bio-inspired structures inspired by the woodpecker’s beak and Balanus, tested at incremental velocities to assess their impact resistance capabilities (Figures 2(a) and 2(b) illustrate the impact direction). Notably, the Balanus-inspired structures demonstrated a significantly higher impulse absorption compared to the woodpecker-inspired structures, as evident from the force-time graphs in Figure 3. This trend was consistent across various impact velocities, highlighting the Balanus-inspired design’s superior performance in dissipating impact energy. These tests not only validate the theoretical models but also provide tangible evidence of the potential improvements in impact resistance offered by bio-inspired designs. The Balanus-inspired structures demonstrated remarkable impact absorption capabilities, reinforcing the concept that natural designs can be effectively translated into protective gear with superior performance characteristics (Reference Ha and LuFischer et al., 2010; Reference Fischer, Thielen, Loprang, Seidel, Fleck, Speck and Bührig-PolaczekSan Ha & Lu, 2020).
4.2. Numerical analysis results
To further elucidate the experimental findings, a numerical analysis was conducted, spanning explicit dynamics and static structural analysis. This multi-phase approach aimed to explore the underlying factors contributing to the observed performance variation between the Balanus and woodpecker-inspired designs. Figure 4 (a) to (d) illustrate the CAD models of unit repetitive and single-strip structures used for explicit dynamic and static structural analysis. The numerical analysis, encompassing both explicit dynamics and static structural assessments, offers a comprehensive understanding of the intrinsic properties contributing to the efficacy of bio-inspired designs (Reference Letov and ZhaoLetov & Fiona Zhao, 2023), (Reference Najmon, Jacob, Wood and TovarNajmon et al., 2018). This analytical approach not only supports the physical testing outcomes but also provides deeper insights into the material and structural differences that support the enhanced performance of these designs. Through these simulations, the superior energy absorption and stress distribution characteristics of the Balanus-inspired designs were elucidated, highlighting the advanced protective capabilities that can be achieved by emulating nature’s resilience.
Illustrations showing the impact direction on the two designs, (a) Woodpecker’s beak-inspired and (b) Balanus-inspired structures, (c) the Woodpecker beak-inspired structure of the helmet liner with gradient porosity that is mimicked by a Schwarz Primitive surface and (d) the Balanus-inspired structure of the helmet liner, (e) representation of the base and (f) the surface of the Balanus-inspired structure with corrugations, (g) 3D printed bio-inspired structures using Formlabs Biomed Amber under the testing equipment of Biokinetics (h) Balanus-inspired structure, (i) Woodpecker-inspired structure, (j) crushed samples of Balanus-inspired structure, (k) crushed sample of woodpecker-inspired structure, (l) Crushed samples of slender 3D printers
Force vs. time graphs obtained from the impact testing of bio-inspired structures with the velocities of (a) 3.96 m/s, (b) 3.98 m/s, (c) 4.84 m/s, and (d) 5.61 m/s
4.2.1. Simulation setup in ANSYS
The numerical analysis was conducted in ANSYS (student), leveraging the explicit dynamics and static structural solvers to simulate real-world impact scenarios: The explicit dynamics analysis phase involved simulating impacts at various velocities on unit strips of the designs, assessing their deformation, stress distribution, and energy absorption under dynamic conditions (Reference Najmon, Jacob, Wood and TovarNajmon et al., 2018). Additional analyses were performed under static conditions on single strips and unit-repetitive structures, evaluating their mechanical responses to incremental loads to understand their structural behavior and resilience (Reference Li, Liao, Dai and XieLi et al., 2019). A mesh convergence study was conducted to ensure the reliability of the simulation results, optimizing the mesh size to achieve a balance between computational efficiency and result accuracy (Reference Dayyani, Shaw, Flores and FriswellDayyani et al., 2015).
Illustrations of structures used for explicit dynamics and static structural analysis a) Unit repetitive structure of the woodpecker-inspired structure for static analysis; b) Unit repetitive structure of the Balanus-inspired structure for static analysis; c) Single-strip Woodpecker-inspired structure and the impactor for explicit dynamic analysis; d) Single- strip Balanus-inspired structure and the impactor for explicit dynamic analysis
Explicit dynamics analysis
Initial simulations focused on moderate and high-velocity impacts on unit strips of both designs. The Balanus-inspired structures exhibited enhanced deformation capabilities and lower maximum equivalent stresses compared to their woodpecker-inspired counterparts. The equivalent stress experienced by the Balanus-inspired and Woodpecker-inspired structures at 15 m/s are 2.78 · 107 Pa, 5.06 · 107 Pa, and at 60 m/s are 5.02 · 107 Pa and 2.56 · 108 Pa respectively. Figures 6 a, 6 b, and 6 c show explicit dynamic test results for moderate (6–15 m/s) and high (40–60 m/s) impact velocities v. These results suggest a more efficient energy absorption mechanism inherent to the Balanus design, even when subjected to high-impact velocities.
4.2.3. Static structural analysis
Subsequent static analysis on single strips under incremental loads further confirmed the superior performance of the Balanus design. The static analysis was performed under incrementally varying load conditions at 5000 N, 7500 N, and 10000 N respectively. The Balanus-inspired structures demonstrated lower total deformation and equivalent stress across all loading conditions. The maximum equivalent stress experienced by the Balanus and Woodpecker-inspired structures at a load of 10000 N are 1.58 · 109 Pa and 1.32 · 1010 Pa respectively. Figures 6 d, e, f, g, and h show the static structural analysis results which indicate robust structural integrity conducive to impact resistance.
4.2.4. Unit-repetitive structure analysis
Focusing on unit-repetitive structures, the static-structural analysis revealed consistent trends, with Balanus-inspired designs outperforming the woodpecker-inspired structures in terms of deformation and stress distribution as depicted in Figure 6 d, e, f, g, and h with dashed lines, thus visually depicting the minimal deformation in the Balanus-inspired designs, emphasizing their superior structural efficiency. The structural analysis was performed under incrementally varying conditions at 5000 N, 7500 N, and 10000 N respectively. The maximum equivalent stress experienced by the unit-repetitive Balanus and Woodpecker-inspired structures at 10000 N load conditions are 9.68 · 108 Pa, and 1.27 · 1010 Pa respectively. The Woodpecker-inspired structure experiences higher stress at the regions of higher porosity and is prone to failure at a faster rate. This observation using numerical analysis supports the results acquired through physical experimentation.
5. Discussion and conclusion
Empirical and numerical analyses highlight the superior impact resistance of Balanus-inspired structures over woodpecker-inspired designs. While the woodpecker’s cranial and beak morphology enables it to withstand repetitive high-velocity impacts (Reference Najmon, Jacob, Wood and TovarNajmon et al., 2018). This biological marvel inspires the design of helmet liners that can offer similar protective benefits for human users, particularly in scenarios involving abrupt head movements or collisions. Balanus shells’ conical shape and corrugated exterior provide exceptional resistance to compressive forces and extreme marine stresses (Reference Tuzgel, Akbulut, Guzel, Yucesoy, Sahin, Tasdemirci and GudenSPIVEY, 1988; Reference Wang, Chen, Roy and SilberschmidtTuzgel et al., 2022). Applying these bioinspired principles to helmet liners enhances their ability to absorb and dissipate impact energy, reducing injury risks. Tests show Balanus-inspired designs achieve higher impulse resistance and lower stress levels compared to woodpecker-inspired structures, making them more effective for impact protection. Two key factors contribute to the superior performance of the Balanus-inspired structure:
1. Surface Corrugations: The conical structure's surface corrugations delay elastic buckling by distributing stresses more effectively. A comprehensive review of corrugated structures shows that local corrugations significantly enhance stability under load (Reference Dayyani, Shaw, Flores and FriswellDayyani et al., 2015).
2. Higher Stiffness-to-Weight Ratio: Increased structural hierarchy, resulting from additional corrugations, raises the stiffness-to-weight ratio, improving stability and resistance to buckling. Studies report that higher-order hierarchical sandwich structures exhibit better strength than the first-order corrugated structures, significantly increasing the critical buckling load and overall shell stability (Reference Dayyani, Shaw, Flores and FriswellDayyani et al., 2015).
Higher order corrugated structure: the conical structure represents first-order corrugations (depicted in red), and the surface corrugations represent the second order corrugations (depicted in blue)
Numerical analysis results: explicit dynamics analysis results of (a) deformation Δ, (b) maximum von Mises stress σvm, (c) maximum equivalent strain εeq; static structural analysis of (d) deformation Δ, (e) maximum von Mises stress σvm, (f) maximum equivalent strain εeq, (g) principal stress σmax, and (h) principal strain εmax
Figure 5 visually explains the second-order corrugations of the Balanus-inspired structure. The first-order corrugation is the conical shape of the Balanus-inspired structure as depicted in colour red, and additional corrugations on the surface of the conical shape represent the second-order corrugated structure as depicted in blue. It could be argued that the woodpecker’s beak-inspired structure also possesses a second-order hierarchical nature, considering the two changes in porosity within it, from 35% to 65% and vice versa. However, in such instances, an additional factor, namely the stiffness-to-weight ratio, plays a critical role in determining effective impact resistance. The comparison of the stiffness-to-weight ratios was estimated in this work through k/V at loads 5000 N and 10000 N, where k = F/δ is stiffness, F is the force acting on the structure, δ is the deformation of the body, and V is the volume of the structure as the material remains the same. k/V = 2.45 × 1012 Nm for the Balanus-inspired structure and k/V = 2.45 × 1012 Nm for the woodpecker-inspired structure. Empirical and numerical results helped identify key parameters for selecting between biological features with different geometries that exhibit similar functions.
Acknowledgements
We sincerely thank Chris Whitehall of Biokinetics and Associates LTD, Ottawa, Canada for the experimental setup and the guidance for the experiments. This research work is supported by the Natural Sciences and Engineering Research Council of Canada Discovery Grant RGPIN-2018-05971 and the McGill Engineering Doctoral Award (MEDA).
Data Availability
The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.
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