Biomechanical properties of insect wings: the stress stiffening effects on the asymmetric bending of the Allomyrina dichotoma beetle's hind wing

Tensile mechanical properties and finite element simulation of the wings of the butterfly Tirumala limniace

This study examined the morphological characteristics and mechanical properties of the wings of Tirumala limniace. The wings of this butterfly, including the forewings and hindwings, are composed mainly of a flexible wing membrane and supporting wing veins. Scanning electron microscopy was employed to observe specific positions of the wing membrane and veins and reveal the morphological characteristics. Tensile experiments were conducted to evaluate the mechanical properties of the wings and proved that the multifiber layer structures have a significantly fixed orientation of fiber alignment. A butterfly wing model reconstructed in reverse based on the finite element method was used to analyze the static characteristics of the wing structure in detail. Evaluation of stress and strain after applying uniform loading, perpendicular loading, and torsion revealed that minor wing deformation occurred and was concentrated near the main wing vein, which verifies the steadiness of the butterfly wing structure. Additionally, the flapping of butterfly wings was simulated using computational fluid dynamics to study the flow field near the butterfly wings and the distribution of pressure gradient on the wings. The results confirmed the effect of wing veins on maintaining the flight performance.

Numerical Simulations of the Effect of the Asymmetrical Bending of the Hindwings of a Hovering C. buqueti Bamboo Weevil with Respect to the Aerodynamic Characteristics

The airfoil structure and folding pattern of the hindwings of a beetle provide new transformation paths for improvements in the aerodynamic performance and structural optimization of flapping-wing flying robots. However, the explanation for the aerodynamic mechanism of the asymmetrical bending of a real beetle's hindwings under aerodynamic loads originating from the ventral and dorsal sides is unclear. To address this gap in our understanding, a computational investigation into the aerodynamic characteristics of the flight ability of C. buqueti and the large folding ratio of their hindwings when hovering is carried out in this article. A three-dimensional (3D) pressure-based SST k-ω turbulence model with a biomimetic structure was used for the detailed analysis, and a refined polyhedral mesh was used for the simulations. The results show that the fluid around the hindwings forms a vortex ring consisting of a leading-edge vortex (LEV), wing-tip vortex (TV) and trailing-edge vortex (TEV). Approximately 61% of the total lift is generated during the downstroke, which may be closely related to the asymmetric bending of the hindwings when they are subjected to pressure load.

Exploratory Analysis of Color Forms' Variability in the Invasive Asian Lady Beetle Harmonia axyridis (Pallas 1773)

The Asian ladybird (Harmonia axyridis Pallas), native to Asia, is one of the 100 most invasive species in the world and has spread worldwide. This study aimed to characterize color forms of H. axyridis in Croatia and to analyze the variability of wing shape between populations and indicated forms. Geometric morphometric methods were used to analyze a total of 129 left and right wings in males and 126 left and right wings in females of H. axyridis collected from four different sites in Croatia. The results show a significant difference in wing shapes between the studied forms. Each form had its own specific morphotype that likely originated under the influence of genetic changes in the species. This study demonstrates that the use of geometric morphometric analysis is effective in studying the variability in H. axyridis populations. As this study is the first of its kind, for further clarity, it is necessary to conduct additional studies on a larger number of sites and an equal number of individuals of all forms.

Printed miniature robotic actuators with curvature-induced stiffness control inspired by the insect wing

Stimuli-responsive actuating materials offer a promising way to power insect-scale robots, but a vast majority of these material systems are too soft for load bearing in different applications. While strategies for active stiffness control have been developed for humanoid-scale robots, for insect-scale counterparts for which compactness and functional complexity are essential requirements, these strategies are too bulky to be applicable. Here, we introduce a method whereby the same actuating material serves not only as the artificial muscles to power an insect-scale robot for load bearing, but also to increase the robot stiffness on-demand, by bending it to increase the second moment of area. This concept is biomimetically inspired by how insect wings stiffen themselves, and is realized here with manganese dioxide as a high-performing electrochemical actuating material printed on metallized polycarbonate films as the robot bodies. Using an open-electrodeposition printing method, the robots can be rapidly fabricated in one single step in ∼15 minutes, and they can be electrochemically actuated by a potential of ∼1 V to produce large bending of ∼500° in less than 5 s. With the stiffness enhancement method, fast (∼5 s) and reversible stiffness tuning with a theoretical increment by ∼4000 times is achieved in a micro-robotic arm at ultra-low potential input of ∼1 V, resulting in an improvement in load-bearing capability by about 4 times from ∼10μN to ∼41μN.

A review: Learning from the flight of beetles

Some Coleoptera (popularly referred to as beetles) can fly at a low Reynolds number with their deployable hind wings, which directly enables a low body weight-a good bioinspiration strategy for miniaturization of micro-air vehicles (MAVs). The hind wing is a significant part of the body and has a folding/unfolding mechanism whose unique function benefits from different structures and materials. This review summarizes the actions, factors, and mechanisms of beetle flight and bioinspired MAVs with deployable wings. The elytron controlled by muscles is the protected part for the folded hind wing and influences flight performance. The resilin, the storage material for elasticity, is located in the folding parts. The hind wings' folding/unfolding mechanism and flight performance can be influenced by vein structures of hollow, solid and wrinkled veins, the hemolymph that flows in hollow veins and its hydraulic mechanism, and various mechanical properties of veins. The action of beetle flight includes flapping flight, hovering, gliding, and landing. The hind wing is passively deformed through force and hemolymph, and the attack angle of the hind wing and the nanomechanics of the veins, muscles and mass body determine the flight performance. Based these factors, bioinspired MAVs with a new deployable wing structure and new materials will be designed to be much more effective and miniaturized. The new fuels and energy supply are significant aspects of MAVs.

Combined effects of wrinkled vein structures and nanomechanical properties on hind wing deformation

The veins in the hind wings of the Asian ladybird beetle (Harmonia axyridis) play active roles in flight and in the folding/unfolding of the hind wing. Wrinkled vein structures are located within the bending zone and are used for folding the hind wing. This paper investigates the coupled effect of wrinkled vein structures within the hind wing of H. axyridis on its deformation. Based on the nanomechanical properties of the veins, morphology of the hind wing, surface structures of the veins, and microstructures of the cross sections (including the veins and wing membranes), four 3-D coupling models (Model I and Model II: variably reduced-modulus veins with and without wrinkles, respectively; Model III and Model IV: uniformly reduced-modulus veins with and without wrinkles, respectively) are established. Relative to the bending and twisting model shapes, Model I has much more flexibility during passive deformation to control wing deformations. The simulation results show that both the wrinkled structures in the bending zone and the variably reduced modulus of the veins contribute to the flight performance (the bending and twisting deformations) of the hind wings, which has important implications for the design of the deployable wings of micro air vehicles (MAVs).

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.

Structural characteristics analysis of the hind wings in a bamboo weevil (Cyrtotrachelus buqueti)

The finite element method is a powerful tool for evaluating the experimental results. It can help to study the flight mechanism of insects and the structural characteristics of flying wings. Therefore, the research object based on the hind wings of Cyrtotrachelus buqueti (C. buqueti) was completed here. A finite element model with a length of 45 mm in the spanwise direction and a 16 mm width in the chordwise direction were established. We used a three-dimensional (3D) scanner to scan a real hind wing to obtain point cloud images. The physical model of the hind wing was carried out by using both the software Imageware and Unigraphics NX. To quantify the quality of the finite element model of the hind wing, the material properties of the wing membranes and veins were conducted by the tensile testing machine. The structural static properties of the hind wing, including static characteristics analysis and natural vibration modal analysis, were analysed by ANSYS; the stress and deflection under uniformly distributed load, bending moment, and torque were, respectively, shown. It was found that the model only had a small deformation, which shows that the hind wings of C. buqueti have excellent structural properties.

Codling Moth Wing Morphology Changes Due to Insecticide Resistance

The codling moth (CM) (Cydia pomonella L.) is the most important apple pest in Croatia and Europe. Owing to its economic importance, it is a highly controlled species and the intense selection pressure the species is under has likely caused it to change its phenotype in response. Intensive application of chemical-based insecticide treatments for the control of CM has led to resistance development. In this study, the forewing morphologies of 294 CM (11 populations) were investigated using geometric morphometric procedures based on the venation patterns of 18 landmarks. Finite element method (FEM) was also used to further investigate the dispersal capabilities of moths by modelling wing deformation versus wind speed. Three treatments were investigated and comprised populations from integrated and ecological (susceptible) orchards and laboratory-reared non-resistant populations. Forewing shape differences were found among the three treatment populations investigated. Across all three population treatments, the movement of landmarks 1, 7, 8, 9, and 12 drove the wing shape differences found. A reliable pattern of differences in forewing shape as related to control practice type was observed. FEM revealed that as wind speed (m/s^-1) increased, so too did wing deformation (mm) for CM from each of the three treatments modelled. CM from the ecological orchards displayed the least deformation followed by integrated then laboratory-reared CM, which had the highest wing deformation at the highest wind speeds. This study presents an affordable and accessible technique that reliably demonstrates wing shape differences, and thus its use as a population biomarker to detect resistance should be further investigated.

Functional morphology and structural characteristics of the hind wings of the bamboo weevil Cyrtotrachelus buqueti (Coleoptera, Curculionidae)

Research data of the microstructure and surface morphology of insect wings have been used to help design micro air vehicles (MAV) and coating materials. The present study aimed to examine the microstructure and morphology of the hind wings of Cyrtotrachelus buqueti using inverted fluorescence microscopy (IFM), scanning electron microscopy (SEM), and a mechanical testing system. IFM was used to investigate the distribution of resilin in the hind wing, and SEM was performed to assess the functional characteristics and cross-sectional microstructure of the wings. Moreover, mechanical properties regarding the intersecting location of folding lines and the bending zone (BZ) were examined. Resilin, a rubber-like protein, was found in several mobile joints and in veins walls that are connected to the wing membranes. Taken together, structural data, unfolding motions, and results of tensile testing suggest two conclusions on resilin in the hind wing of C. buqueti: firstly, the resilin distribution is likely associated with specific folding mechanisms of the hind wings, and secondly, resilin occurs at positions where additional elasticity is needed, such as in the bending zone, in order to prevent structural damage during repeated folding and unfolding of the hind wings. The functional significance of resilin joints may shed light on the evolutionary relationship between morphological and structural hind wing properties.

Computational biomechanical analyses demonstrate similar shell-crushing abilities in modern and ancient arthropods

The biology of the American horseshoe crab, Limulus polyphemus, is well documented-including its dietary habits, particularly the ability to crush shell with gnathobasic walking appendages-but virtually nothing is known about the feeding biomechanics of this iconic arthropod. Limulus polyphemus is also considered the archetypal functional analogue of various extinct groups with serial gnathobasic appendages, including eurypterids, trilobites and other early arthropods, especially Sidneyia inexpectans from the mid-Cambrian (508 Myr) Burgess Shale of Canada. Exceptionally preserved specimens of S. inexpectans show evidence suggestive of durophagous (shell-crushing) tendencies-including thick gnathobasic spine cuticle and shelly gut contents-but the masticatory capabilities of this fossil species have yet to be compared with modern durophagous arthropods. Here, we use advanced computational techniques, specifically a unique application of 3D finite-element analysis (FEA), to model the feeding mechanics of L. polyphemus and S. inexpectans: the first such analyses of a modern horseshoe crab and a fossil arthropod. Results show that mechanical performance of the feeding appendages in both arthropods is remarkably similar, suggesting that S. inexpectans had similar shell-crushing capabilities to L. polyphemus This biomechanical solution to processing shelly food therefore has a history extending over 500 Myr, arising soon after the first shell-bearing animals. Arrival of durophagous predators during the early phase of animal evolution undoubtedly fuelled the Cambrian 'arms race' that involved a rapid increase in diversity, disparity and abundance of biomineralized prey species.

Morphology of hindwing veins in the shield bug Graphosoma italicum (Heteroptera: Pentatomidae)

Light, fluorescence, and electron microscopy were applied to cross sections and -breakage and whole-mount preparations of the anterior hindwing vein of the shield bug Graphosoma italicum. These analyses were complemented by investigations of the basal part of the forewing Corium and Clavus. The integration of structural, histological, and fluorescence data revealed a complex arrangement of both rigid and elastic structures in the wall of wing veins and provided insights into the constitution of transition zones between rigid and elastic regions. Beneath the exocuticular layers, which are continuous with the dorsal and ventral cuticle of the wing membrane, the lumen of the veins is encompassed by a mesocuticular layer, an internal circular exocuticular layer, and an internal longitudinal endocuticular layer. Separate parallel lumina within the anterior longitudinal vein of the hindwing, arranged side-by-side rostro-caudally, suggest that several veins have fused in the phylogenetic context of vein reduction in the pentatomid hindwing. Gradual structural transition zones and resilin enrichment between sclerotized layers of the vein wall and along the edges of the claval furrow are interpreted as mechanical adaptations to enhance the reliability and durability of the mechanically stressed wing veins.

Hindwings of insects as concept generator for hingeless foldable shading systems

Hingeless shading systems inspired by nature are increasingly the focus of architectural research. In contrast to traditional systems, these compliant mechanisms can reduce the amount of maintenance-intensive parts and can easily be adapted to irregular, doubly curved, facade geometries. Previous mechanisms rely merely on the reversible material deformation of composite structures with almost homogeneous material properties. This leads to large actuation forces and an inherent conflict between the requirements of movement and the capacity to carry external loads. To enhance the performance of such systems, current research is directed at natural mechanisms with concentrated compliance and distinct hinge zones with high load-bearing capacity. Here, we provide insights into our biological findings and the development of a deployable structure inspired by the Flexagon model of hindwings of insects in general and the hierarchical structure of the wing cuticle of the shield bug (Graphosoma lineatum). By using technical fibre-reinforced plastics in combination with an elastomer foil, natural principles have been partially transferred into a multi-layered structure with locally adapted stiffness. Initial small prototypes have been produced in a vacuum-assisted hot press and sustain this functionality. Initial theoretical studies on test surfaces outline the advantages of these bio-inspired structures as deployable external shading systems for doubly curved facades.

Allometry of wing twist and camber in a flower chafer during free flight: How do wing deformations scale with body size?

Intraspecific variation in adult body mass can be particularly high in some insect species, mandating adjustment of the wing's structural properties to support the weight of the larger body mass in air. Insect wings elastically deform during flapping, dynamically changing the twist and camber of the relatively thin and flat aerofoil. We examined how wing deformations during free flight scale with body mass within a species of rose chafers (Coleoptera: Protaetia cuprea) in which individuals varied more than threefold in body mass (0.38-1.29 g). Beetles taking off voluntarily were filmed using three high-speed cameras and the instantaneous deformation of their wings during the flapping cycle was analysed. Flapping frequency decreased in larger beetles but, otherwise, flapping kinematics remained similar in both small and large beetles. Deflection of the wing chord-wise varied along the span, with average deflections at the proximal trailing edge higher by 0.2 and 0.197 wing lengths compared to the distal trailing edge in the downstroke and the upstroke, respectively. These deflections scaled with wing chord to the power of 1.0, implying a constant twist and camber despite the variations in wing and body size. This suggests that the allometric growth in wing size includes adjustment of the flexural stiffness of the wing structure to preserve wing twist and camber during flapping.

Allometry of wing twist and camber in a flower chafer during free flight: How do wing deformations scale with body size?

Intraspecific variation in adult body mass can be particularly high in some insect species, mandating adjustment of the wing's structural properties to support the weight of the larger body mass in air. Insect wings elastically deform during flapping, dynamically changing the twist and camber of the relatively thin and flat aerofoil. We examined how wing deformations during free flight scale with body mass within a species of rose chafers (Coleoptera: Protaetia cuprea) in which individuals varied more than threefold in body mass (0.38-1.29 g). Beetles taking off voluntarily were filmed using three high-speed cameras and the instantaneous deformation of their wings during the flapping cycle was analysed. Flapping frequency decreased in larger beetles but, otherwise, flapping kinematics remained similar in both small and large beetles. Deflection of the wing chord-wise varied along the span, with average deflections at the proximal trailing edge higher by 0.2 and 0.197 wing lengths compared to the distal trailing edge in the downstroke and the upstroke, respectively. These deflections scaled with wing chord to the power of 1.0, implying a constant twist and camber despite the variations in wing and body size. This suggests that the allometric growth in wing size includes adjustment of the flexural stiffness of the wing structure to preserve wing twist and camber during flapping.

How two-dimensional bending can extraordinarily stiffen thin sheets

Curved thin sheets are ubiquitously found in nature and manmade structures from macro- to nanoscale. Within the framework of classical thin plate theory, the stiffness of thin sheets is independent of its bending state for small deflections. This assumption, however, goes against intuition. Simple experiments with a cantilever sheet made of paper show that the cantilever stiffness largely increases with small amounts of transversal curvature. We here demonstrate by using simple geometric arguments that thin sheets subject to two-dimensional bending necessarily develop internal stresses. The coupling between the internal stresses and the bending moments can increase the stiffness of the plate by several times. We develop a theory that describes the stiffness of curved thin sheets with simple equations in terms of the longitudinal and transversal curvatures. The theory predicts experimental results with a macroscopic cantilever sheet as well as numerical simulations by the finite element method. The results shed new light on plant and insect wing biomechanics and provide an easy route to engineer micro- and nanomechanical structures based on thin materials with extraordinary stiffness tunability.

Morphological and mechanical characterisation of the hindwing nodus from the Libellulidae family of dragonfly (Indonesia)

In this communication, the morphologies and mechanical characteristics of nodi from the hindwings of seven Indonesian Libellulidae dragonfly species are identified. Geometrical analyses reveal that in all species, the shape of dorsal face resilin is relatively long and thin while ventral face resilin covers a greater surface area than dorsal face resilin, and is shaped like a hook. Finite element analyses reveal that the magnitude of strain energy may differ considerably between species, even though the locations of highest strain energy are usually the same. Importantly, a correlation is found to exist between the mechanical forces that build up in the resilin, the face under investigation (dorsal or ventral) and the elongational shape factor of the resilin.