Basal Complex and Basal Venation of Odonata Wings: Structural Diversity and Potential Role in the Wing Deformation

Complexity biomechanics: a case study of dragonfly wing design from constituting composite material to higher structural levels

Presenting a novel framework for sustainable and regenerative design and development is a fundamental future need. Here we argue that a new framework, referred to as complexity biomechanics, which can be used for holistic analysis and understanding of natural mechanical systems, is key to fulfilling this need. We also present a roadmap for the design and development of intelligent and complex engineering materials, mechanisms, structures, systems, and processes capable of automatic adaptation and self-organization in response to ever-changing environments. We apply complexity biomechanics to elucidate how the different structural components of a complex biological system as dragonfly wings, from ultrastructure of the cuticle, the constituting bio-composite material of the wing, to higher structural levels, collaboratively contribute to the functionality of the entire wing system. This framework not only proposes a paradigm shift in understanding and drawing inspiration from natural systems but also holds potential applications in various domains, including materials science and engineering, biomechanics, biomimetics, bionics, and engineering biology.

Little bits of dragonfly history repeating exemplified by a new Pennsylvanian family

During its 320 Myr evolution, dragon- and damselfly (Odonata) wing morphology underwent intense modifications. The resulting diversity prompted comparative analyses focusing on phylogeny. However, homoplasy proved to plague wing-related characters. Concurrently, limited benefits were obtained from considering fossil taxa, similarly impacted. Herein, we investigate two aspects particularly affected by convergence, namely the acquisition of vein-like structuring elements derived from regular cross-venation, termed conamina; and the evolution of butter knife wing shape. Conamen implementation is found to be consistently linked with vein curvature sharpening, itself generating potential breaking points. Conamina therefore likely evolved to address wing integrity issues during ever-more-demanding flight performance. Moreover, an existing conamen is likely to trigger the acquisition of further, associated conamina. As for butter knife shape, previously documented in the extinct Archizygoptera and among damselflies, we report a new, 315 Ma occurrence with the rare species Haidilaozhen cuiae gen. et sp. nov. (family Haidilaozhenidae fam. nov.), from the Xiaheyan locality (China). The repeated acquisition of butter knife-shaped wing can be related to slow speed flight and, in turn, predator avoidance. In both cases of iterated regularities, the unique 'network-and-membrane' wing design proper to insects is found to compose a strong, constraining factor.

Basal complex: a smart wing component for automatic shape morphing

Insect wings are adaptive structures that automatically respond to flight forces, surpassing even cutting-edge engineering shape-morphing systems. A widely accepted but not yet explicitly tested hypothesis is that a 3D component in the wing's proximal region, known as basal complex, determines the quality of wing shape changes in flight. Through our study, we validate this hypothesis, demonstrating that the basal complex plays a crucial role in both the quality and quantity of wing deformations. Systematic variations of geometric parameters of the basal complex in a set of numerical models suggest that the wings have undergone adaptations to reach maximum camber under loading. Inspired by the design of the basal complex, we develop a shape-morphing mechanism that can facilitate the shape change of morphing blades for wind turbines. This research enhances our understanding of insect wing biomechanics and provides insights for the development of simplified engineering shape-morphing systems.

Golden ratio in venation patterns of dragonfly wings

The vein pattern in insect wings allows this lightweight structure to carry multiple biological functions. Here, an investigation of the angular distribution of the vein struts in dragonfly wings revealed that the golden angle or golden ratio dominates the venation patterns. We find that the golden angle dominates the intervein angles in regions where thin veins and membranes demand strength reinforcement. A golden ratio partition method has thus been developed that explains a set of preferred intervein angles in distorted polygon-shaped venation cells throughout the venation pattern in dragonfly wings. These observations provide new evidence that the wing structure is spatially optimized, by the golden rule in nature, for supporting biomechanical functions of dragonfly wings.

Dragonfly-Inspired Wing Design Enabled by Machine Learning and Maxwell's Reciprocal Diagrams

This research is taking the first steps toward applying a 2D dragonfly wing skeleton in the design of an airplane wing using artificial intelligence. The work relates the 2D morphology of the structural network of dragonfly veins to a secondary graph that is topologically dual and geometrically perpendicular to the initial network. This secondary network is referred as the reciprocal diagram proposed by Maxwell that can represent the static equilibrium of forces in the initial graph. Surprisingly, the secondary graph shows a direct relationship between the thickness of the structural members of a dragonfly wing and their in-plane static equilibrium of forces that gives the location of the primary and secondary veins in the network. The initial and the reciprocal graph of the wing are used to train an integrated and comprehensive machine-learning model that can generate similar graphs with both primary and secondary veins for a given boundary geometry. The result shows that the proposed algorithm can generate similar vein networks for an arbitrary boundary geometry with no prior topological information or the primary veins' location. The structural performance of the dragonfly wing in nature also motivated the authors to test this research's real-world application for designing the cellular structures for the core of airplane wings as cantilever porous beams. The boundary geometry of various airplane wings is used as an input for the design proccedure. The internal structure is generated using the training model of the dragonfly veins and their reciprocal graphs. One application of this method is experimentally and numerically examined for designing the cellular core, 3D printed by fused deposition modeling, of the airfoil wing; the results suggest up to 25% improvements in the out-of-plane stiffness. The findings demonstrate that the proposed machine-learning-assisted approach can facilitate the generation of multiscale architectural patterns inspired by nature to form lightweight load-bearable elements with superior structural properties.

Insect wing 3D printing

Insects have acquired various types of wings over their course of evolution and have become the most successful terrestrial animals. Consequently, the essence of their excellent environmental adaptability and locomotive ability should be clarified; a simple and versatile method to artificially reproduce the complex structure and various functions of these innumerable types of wings is necessary. This study presents a simple integral forming method for an insect-wing-type composite structure by 3D printing wing frames directly onto thin films. The artificial venation generation algorithm based on the centroidal Voronoi diagram, which can be observed in the wings of dragonflies, was used to design the complex mechanical properties of artificial wings. Furthermore, we implemented two representative functions found in actual insect wings: folding and coupling. The proposed crease pattern design software developed based on a beetle hindwing enables the 3D printing of foldable wings of any shape. In coupling-type wings, the forewing and hindwing are connected to form a single large wing during flight; these wings can be stored compactly by disconnecting and stacking them like cicada wings.

Triple Stiffness: A Bioinspired Strategy to Combine Load-Bearing, Durability, and Impact-Resistance

Structures with variable stiffness have received increasing attention in the fields of robotics, aerospace, structural, and biomedical engineering. This is because they not only adapt to applied loads, but can also combine mutually exclusive properties. Here inspired by insect wings, the concept of "triple stiffness" is introduced and applied to engineering systems that exhibit three distinct deformability regimes. By implementing "flexible joints," "mechanical stoppers," and "buckling zones," structures are engineered to be not only load-bearing and durable, but also impact-resistant. To practice the performance of the design concept in real-life applications, the developed structures are integrated into 3D printed airplane wing models that withstood collisions without failure. The concept developed here opens new avenues for the development of structural elements that are load-bearing, durable, and impact-resistant at the same time.

Effects of pterostigma structure on vibrational characteristics during flight of Asian ladybird Harmonia axyridis (Coleoptera: Coccinellidae)

The hind wings of beetles are deployable and play an essential role in flight. In the Asian ladybird Harmonia axyridis (Coleoptera: Coccinellidae), the pterostigma (pst) is found in the middle of the hind wing instead of at the tip of the hind wing. This paper investigates the effect of the pst on the vibrational characteristics during the flight of H. axyridis. Based on cross sections of the pst and veins as well as the morphology and nanomechanical properties of the hind wing, including the wing membrane and veins, three three-dimensional coupling models, Models I-III, of hind wings with/without pst structures and veins with varying or uniform reduced moduli are established. Modal analysis results for these three models show that the vibrational characteristics and deformation tendencies change the flight performance of the hind wing models with pst structures compared with that of the other models. The results in this paper reveal that the pst structure has an important influence on vibrational characteristics and deformation tendencies and, hence, on flight performance; the relationships between the body mass and the area of the hind wing, which have significant implications for the design of biomimetic deployable wing structures for micro air vehicles (MAVs), are also analyzed.

Insect wing damage: causes, consequences and compensatory mechanisms

The evolution of wings has played a key role in the success of insect species, allowing them to diversify to fill many niches. Insect wings are complex multifunctional structures, which not only have to withstand aerodynamic forces but also need to resist excessive stresses caused by accidental collisions. This Commentary provides a summary of the literature on damage-reducing morphological adaptations in wings, covering natural causes of wing collisions, their impact on the structural integrity of wings and associated consequences for both insect flight performance and life expectancy. Data from the literature and our own observations suggest that insects have evolved strategies that (i) reduce the likelihood of wing damage and (ii) allow them to cope with damage when it occurs: damage-related fractures are minimized because wings evolved to be damage tolerant and, in the case of wing damage, insects compensate for the reduced aerodynamic efficiency with dedicated changes in flight kinematics.

Phylogeny of Libellulidae (Odonata: Anisoptera): comparison of molecular and morphology-based phylogenies based on wing morphology and migration

Background

Establishing the species limits and resolving phylogenetic relationships are primary goals of taxonomists and evolutionary biologists. At present, a controversial question is about interspecific phylogenetic information in morphological features. Are the interspecific relationships established based on genetic information consistent with the traditional classification system? To address these problems, this study analyzed the wing shape structure of 10 species of Libellulidae, explored the relationship between wing shape and dragonfly behavior and living habits, and established an interspecific morphological relationship tree based on wing shape data. By analyzing the sequences of mitochondrial COI gene and the nuclear genes 18S, 28S rRNA and ITS in 10 species of dragonflies, the interspecific relationship was established.

Method

The wing shape information of the male forewings and hindwings was obtained by the geometric morphometrics method. The inter-species wing shape relationship was obtained by principal component analysis (PCA) in MorphoJ1.06 software. The inter-species wing shape relationship tree was obtained by cluster analysis (UPGMA) using Mesquite 3.2 software. The COI, 18S, ITS and 28S genes of 10 species dragonfly were blasted and processed by BioEdit v6 software. The Maximum Likelihood(ML) tree was established by raxmlGUI1.5b2 software. The Bayes inference (BI) tree was established by MrBayes 3.2.6 in Geneious software.

Results

The main difference in forewings among the 10 species of dragonfly was the apical, radial and discoidal regions dominated by the wing nodus. In contrast, the main difference among the hindwings was the apical and anal regions dominated by the wing nodus. The change in wing shape was closely related to the ability of dragonfly to migrate. The interspecific relationship based on molecular data showed that the species of Orthetrum genus branched independently of the other species. Compared to the molecular tree of 10 species, the wing shape clustering showed some phylogenetic information on the forewing shape (with large differences on the forewing shape tree vs. molecular tree), and there was no interspecific phylogenetic information of the hindwing shape tree vs. molecular tree.

Conclusion

The dragonfly wing shape characteristics are closely related to its migration ability. Species with strong ability to migrate have the forewing shape that is longer and narrower, and have larger anal region, whereas the species that prefer short-distance hovering or standing still for a long time have forewing that are wider and shorter, and the anal region is smaller. Integrating morphological and molecular data to evaluate the relationship among dragonfly species shows there is some interspecific phylogenetic information in the forewing shape and none in the hindwing shape. The forewing and hindwing of dragonflies exhibit an inconsistent pattern of morphological changes in different species.

Both stiff and compliant: morphological and biomechanical adaptations of stick insect antennae for tactile exploration

Active tactile exploration behaviour is constrained to a large extent by the morphological and biomechanical properties of the animal's somatosensory system. In the model organism Carausius morosus, the main tactile sensory organs are long, thin, seemingly delicate, but very robust antennae. Previous studies have shown that these antennae are compliant under contact, yet stiff enough to maintain a straight shape during active exploration. Overcritical damping of the flagellum, on the other hand, allows for a rapid return to the straight shape after release of contact. Which roles do the morphological and biomechanical adaptations of the flagellum play in determining these special mechanical properties? To investigate this question, we used a combination of biomechanical experiments and numerical modelling. A set of four finite-element (FE) model variants was derived to investigate the effect of the distinct geometrical and material properties of the flagellum on its static (bending) and dynamic (damping) characteristics. The results of our numerical simulations show that the tapered shape of the flagellum had the strongest influence on its static biomechanical behaviour. The annulated structure and thickness gradient affected the deformability of the flagellum to a lesser degree. The inner endocuticle layer of the flagellum was confirmed to be essential for explaining the strongly damped return behaviour of the antenna. By highlighting the significance of two out of the four main structural features of the insect flagellum, our study provides a basis for mechanical design of biomimetic touch sensors tuned to become maximally flexible while quickly resuming a straight shape after contact.

Micro-morphological adaptations of the wing nodus to flight behaviour in four dragonfly species from the family Libellulidae (Odonata: Anisoptera)

Adult dragonflies can be divided into two major groups, perchers and fliers, exhibiting notably different flight behaviour. Previous studies have yielded conflicting results regarding the link between the wing macro-morphology and flight style in these two groups. In this study, we present the first systematic investigation of the micro-morphological differences of wings of percher and flier dragonflies in four closely related species from the family Libellulidae. Our results suggest that the shape and material composition of wing microstructural components and, in particular, the nodus are adapted to facilitate the specific wing functioning in fliers and perchers. The findings further indicate a decreasing trend in the area proportion of the soft resilin-dominated cuticle in the nodus in the series of species from typical perchers to typical fliers. Such a reduction in the resilin proportion in the nodus of fliers is associated with an increase in the wing aspect ratio. The knot-shaped protrusion at the nodus of perchers, which becomes notably smaller in that of strong fliers, is likely to act as a mechanical stopper, avoiding large wing displacements. This study aims to develop a novel framework for future research on the relationship between wing morphology and flight behaviour in dragonflies.

Stiffness distribution in insect cuticle: a continuous or a discontinuous profile?

Insect cuticle is a biological composite with a high degree of complexity in terms of both architecture and material composition. Given the complex morphology of many insect body parts, finite-element (FE) models play an important role in the analysis and interpretation of biomechanical measurements, taken by either macroscopic or nanoscopic techniques. Many previous studies show that the interpretation of nanoindentation measurements of this layered composite material is very challenging. To develop accurate FE models, it is of particular interest to understand more about the variations in the stiffness through the thickness of the cuticle. Considering the difficulties of making direct measurements, in this study, we use the FE method to analyse previously published data and address this issue numerically. For this purpose, sets of continuous or discontinuous stiffness profiles through the thickness of the cuticle were mathematically described. The obtained profiles were assigned to models developed based on the cuticle of three insect species with different geometries and layer configurations. The models were then used to simulate the mechanical behaviour of insect cuticles subjected to nanoindentation experiments. Our results show that FE models with discontinuous exponential stiffness gradients along their thickness were able to predict the stress and deformation states in insect cuticle very well. Our results further suggest that, for more accurate measurements and interpretation of nanoindentation test data, the ratio of the indentation depth to cuticle thickness should be limited to 7% rather than the traditional '10% rule'. The results of this study thus might be useful to provide a deeper insight into the biomechanical consequences of the distinct material distribution in insect cuticle and also to form a basis for more realistic modelling of this complex natural composite.

The probability of wing damage in the dragonfly Sympetrum vulgatum (Anisoptera: Libellulidae): a field study

Dragonfly wings resist millions of cycles of dynamic loading in their lifespan. During their operation, the wings are subjected to relatively high mechanical stresses. They further experience accidental collisions which result from the insects' daily activities, such as foraging, mating and fighting with other individuals. All these factors may lead to irreversible wing damage. Here, for the first time, we collected qualitative and quantitative data to systematically investigate the occurrence of damage in dragonfly wings in nature. The results obtained from the analysis of 119 wings from >30 individual Sympetrum vulgatum (Anisoptera: Libellulidae), collected at the second half of their flight period, indicate a high risk of damage in both fore- and hindwings. Statistical analyses show no significant difference between the extent of damage in fore- and hindwings, or between male and female dragonflies. However, we observe a considerable difference in the probability of damage in different wing regions. The wing damage is found to mainly result from two failure modes: wear and fracture.

Summary: This study provides the first qualitative and quantitative data on the occurrence of damage in the wings of the dragonfly Sympetrum vulgatum in nature. This article has an associated First Person interview with the first author of the paper as part of the supplementary information.

Dragonfly wing nodus: A one-way hinge contributing to the asymmetric wing deformation

Dragonfly wings are highly specialized locomotor systems, which are formed by a combination of several structural components. The wing components, also known as structural elements, are responsible for the various aspects of the wing functionality. Considering the complex interactions between the wing components, modelling of the wings as a whole is only possible with inevitable huge oversimplifications. In order to overcome this difficulty, we have recently proposed a new approach to model individual components of complex wings comparatively. Here, we use this approach to study nodus, a structural element of dragonfly wings which has been less studied to date. Using a combination of several imaging techniques including scanning electron microscopy (SEM), wide-field fluorescence microscopy (WFM), confocal laser scanning microscopy (CLSM) and micro-computed tomography (micro-CT) scanning, we aim to characterize the spatial morphology and material composition of fore- and hindwing nodi of the dragonfly Brachythemis contaminata. The microscopy results show the presence of resilin in the nodi, which is expected to help the deformability of the wings. The computational results based on three-dimensional (3D) structural data suggest that the specific geometry of the nodus restrains its displacements when subjected to pressure on the ventral side. This effect, resulting from an interlocking mechanism, is expected to contribute to the dorso-ventral asymmetry of wing deformation and to provide a higher resistance to aerodynamic forces during the downstroke. Our results provide an important step towards better understanding of the structure-property-function relationship in dragonfly wings.

STATEMENT OF SIGNIFICANCE

In this study, we investigate the wing nodus, a specialized wing component in dragonflies. Using a combination of modern imaging techniques, we demonstrate the presence of resilin in the nodus, which is expected to facilitate the wing deformability in flight. The specific geometry of the nodus, however, seems to restrain its displacements when subjected to pressure on the ventral side. This effect, resulting from an interlocking mechanism, is suggested to contribute to dorso-ventral asymmetry of wing deformations and to provide a higher resistance to aerodynamic forces during the downstroke. Our results provide an important step towards better understanding of the structure-property-function relationship in dragonfly wings and might help to design more efficient wings for biomimetic micro-air vehicles.