H. Rajabi

Effect of microstructure on the mechanical and damping behaviour of dragonfly wing veins

Insect wing veins are biological composites of chitin and protein arranged in a complex lamellar configuration. Although these hierarchical structures are found in many ‘venous wings of insects, very little is known about their physical and mechanical characteristics. For the first time, we carried out a systematic comparative study to gain a better understanding of the influence of microstructure on the mechanical characteristics and damping behaviour of the veins. Morphological data have been used to develop a series of three-dimensional numerical models with different material properties and geometries. Finite-element analysis has been employed to simulate the mechanical response of the models under different loading conditions. The modelling strategy used in this study enabled us to determine the effects selectively induced by resilin, friction between layers, shape of the cross section, material composition and layered structure on the stiffness and damping characteristics of wing veins. Numerical simulations suggest that although the presence of the resilin-dominated endocuticle layer results in a much higher flexibility of wing veins, the dumbbell-shaped cross section increases their bending rigidity. Our study further shows that the rubber-like cuticle, friction between layers and material gradient-based design contribute to the higher damping capacity of veins. The results of this study can serve as a reference for the design of novel bioinspired composite structures.

Resilin microjoints: a smart design strategy to avoid failure in dragonfly wings

Dragonflies are fast and manoeuvrable fliers and this ability is reflected in their unique wing morphology. Due to the specific lightweight structure, with the crossing veins joined by rubber-like resilin patches, wings possess strong deformability but can resist high forces and large deformations during aerial collisions. The computational results demonstrate the strong influence of resilin-containing vein joints on the stress distribution within the wing. The presence of flexible resilin in the contact region of the veins prevents excessive bending of the cross veins and significantly reduces the stress concentration in the joint.

Effects of multiple vein microjoints on the mechanical behaviour of dragonfly wings: numerical modelling.

Dragonfly wings are known as biological composites with high morphological complexity. They mainly consist of a network of rigid veins and flexible membranes, and enable insects to perform various flight manoeuvres. Although several studies have been done on the aerodynamic performance of Odonata wings and the mechanisms involved in their deformations, little is known about the influence of vein joints on the passive deformability of the wings in flight. In this article, we present the first three-dimensional finite-element models of five different vein joint combinations observed in Odonata wings. The results from the analysis of the models subjected to uniform pressures on their dorsal and ventral surfaces indicate the influence of spike-associated vein joints on the dorsoventral asymmetry of wing deformation. Our study also supports the idea that a single vein joint may result in different angular deformations when it is surrounded by different joint types. The developed numerical models also enabled us to simulate the camber formation and stress distribution in the models. The computational data further provide deeper insights into the functional role of resilin patches and spikes in vein joint structures. This study might help to more realistically model the complex structure of insect wings in order to design more efficient bioinspired micro-air vehicles in future.

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.nnnSTATEMENT OF SIGNIFICANCEnIn 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.

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

Dragonflies and damselflies, belonging to the order Odonata, are known to be excellent fliers with versatile flight capabilities. The ability to fly over a wide range of speeds, high manoeuvrability and great agility are a few characteristics of their flight. The architecture of the wings and their structural elements have been found to play a major role in this regard. However, the precise influence of individual wing components on the flight performance of these insects remains unknown. The design of the wing basis (so called basal complex) and the venation of this part are responsible for particular deformability and specific shape of the wing blade. However, the wing bases are rather different in representatives of different odonate groups. This presumably reflects the dimensions of the wings on one hand, and different flight characteristics on the other hand. In this article, we develop the first three-dimensional (3D) finite element (FE) models of the proximal part of the wings of typical representatives of five dragonflies and damselflies families. Using a combination of the basic material properties of insect cuticle, a linear elastic material model and a nonlinear geometric analysis, we simulate the mechanical behaviour of the wing bases. The results reveal that although both the basal venation and the basal complex influence the structural stiffness of the wings, it is only the latter which significantly affects their deformation patterns. The use of numerical simulations enabled us to address the role of various wing components such as the arculus, discoidal cell and triangle on the camber formation in flight. Our study further provides a detailed representation of the stress concentration in the models. The numerical analysis presented in this study is not only of importance for understanding structure-function relationship of insect wings, but also might help to improve the design of the wings for biomimetic micro-air vehicles (MAVs).

How does a slender tibia resist buckling? Effect of material, structural and geometric characteristics on buckling behaviour of the hindleg tibia in stick insect postembryonic development

ABSTRACT During the lifespan of the stick insect Carausius morosus, their long and narrow tibiae experience substantial compressive loads. The mechanical load on the tibiae increases as the weight of the insect rises. The increase in body weight is accompanied by a notable increase in the insects body size and, accordingly, by an increase in the length of the tibiae. Both of these changes can raise the risk of buckling of the tibiae. In this study, we tracked changes in the material and geometric properties of the hindleg tibia of C. morosus during growth. The results show that although buckling (either by Euler buckling or local buckling) is the dominant failure mode under compression, the tibia is very capable of maintaining its buckling resistance in each postembryonic developmental stage. This is essentially the result of a compromise between the increasing slenderness of the tibia and its increasing material stiffness. The use of an optimal radius to thickness ratio, a soft resilin-dominated core, and chitin fibres oriented in both longitudinal and circumferential directions are presumably additional strategies preventing buckling of the tibia. This study, providing the first quantitative data on changes in the biomechanical properties of cuticle during the entire life of an insect, is expected to shed more light on the structure–property–function relationship in this complex biological composite. Summary: Quantitative data on changes in biomechanical properties of hindleg tibia cuticle during the entire life of the stick insect Carausius morosus indicate strategies preventing buckling of the tibia.

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.

Wing cross veins: an efficient biomechanical strategy to mitigate fatigue failure of insect cuticle

Locust wings are able to sustain millions of cycles of mechanical loading during the lifetime of the insect. Previous studies have shown that cross veins play an important role in delaying crack propagation in the wings. Do cross veins thus also influence the fatigue behaviour of the wings? Since many important fatigue parameters are not experimentally accessible in a small biological sample, here we use the finite element (FE) method to address this question numerically. Our FE model combines a linear elastic material model, a direct cyclic approach and the Paris law and shows results which are in very good agreement with previously reported experimental data. The obtained results of our study show that cross veins indeed enhance the durability of the wings by temporarily stopping cracks. The cross veins further distribute the stress over a larger area and therefore minimize stress concentrations. In addition, our work indicates that locust hind wings have an endurance limit of about 40% of the ultimate tensile strength of the wing material, which is comparable to many engineering materials. The comparison of the results of the computational study with predictions of two most commonly used fatigue failure criteria further indicates that the Goodman criterion can be used to roughly predict the failure of the insect wing. The methodological framework presented in our study could provide a basis for future research on fatigue of insect cuticle and other biological composite structures.

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.

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

ABSTRACT 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.