Allometric Scaling Reveals Evolutionary Constraint on Odonata Wing Cellularity via Critical Crack Length

Scaling in insect wings is a complex phenomenon that seems pivotal in maintaining wing functionality. In this study, the relationship between wing size and the size, location, and shape of wing cells in dragonflies and damselflies (Odonata) is investigated, aiming to address the question of how these factors are interconnected. To this end, WingGram, the recently developed computer-vision-based software, is used to extract the geometric features of wing cells of 389 dragonflies and damselfly wings from 197 species and 16 families. It has been found that the cell length of the wings does not depend on the wing size. Despite the wide variation in wing length (8.42 to 56.5 mm) and cell length (0.1 to 8.5 mm), over 80% of the cells had a length ranging from 0.5 to 1.5 mm, which was previously identified as the critical crack length of the membrane of locust wings. An isometric scaling of cells is also observed with maximum size in each wing, which increased as the size increased. Smaller cells tended to be more circular than larger cells. The results have implications for bio-mimetics, inspiring new materials and designs for artificial wings with potential applications in aerospace engineering and robotics.

Organic and inorganic equivalent models for analysis of red blood cell mechanical behaviour

Experimental investigation into the mechanical response of red blood cells is presently impeded with the main impediments being the micro dimensions involved and ethical issues associated with in vivo testing. The widely employed alternative approach of computational modelling suffers from its own inherent limitations being reliant on precise constitutive and boundary information. Moreover, and somewhat critically, numerical computational models themselves are required to be validated by means of experimentation and hence suffer similar impediments. An alternative experimental approach is examined in this paper involving large-scale equivalent models manufactured principally from inorganic, and to lesser extent organic, materials. Although there presently exists no known method providing the means to investigate the mechanical response of red blood cells using scaled models simultaneously having different dimensions and materials, the present paper aims to develop a scaled framework based on the new finite-similitude theory that has appeared in the recent open literature. Computational models are employed to test the effectiveness of the proposed method, which in principle can provide experimental solution methods to a wide range of practical applications including the design of red-blood cell nanorobots and drug delivery systems. By means of experimentally validated numerical experiments under impact loading it is revealed that although exact prediction is not achieved good accuracy can nevertheless be obtained. Furthermore, it is demonstrated how the proposed approach for first time provides a means to relate models at different scales founded on different constitutive equations.

Wing Coupling in Bees and Wasps: From the Underlying Science to Bioinspired Engineering

Wing-to-wing coupling mechanisms synchronize motions of insect wings and minimize their aerodynamic interference. Albeit they share the same function, their morphological traits appreciably vary across groups. Here the structure-material-function relationship of wing couplings of nine castes and species of Hymenoptera is investigated. It is shown that the springiness, robustness, and asymmetric behavior augment the functionality of the coupling by reducing stress concentrations and minimizing the impacts of excessive flight forces. A quantitative link is established between morphological variants of the coupling mechanisms and forces to which they are subjected. Inspired by the coupling mechanisms, a rotating-sliding mechanical joint that withstands tension and compression and can also be locked/unlocked is fabricated. This is the first biomimetic research of this type that integrates approaches from biology and engineering.

WingMesh: A Matlab-Based Application for Finite Element Modeling of Insect Wings

The finite element (FE) method is one of the most widely used numerical techniques for the simulation of the mechanical behavior of engineering and biological objects. Although very efficient, the use of the FE method relies on the development of accurate models of the objects under consideration. The development of detailed FE models of often complex-shaped objects, however, can be a time-consuming and error-prone procedure in practice. Hence, many researchers aim to reach a compromise between the simplicity and accuracy of their developed models. In this study, we adapted Distmesh2D, a popular meshing tool, to develop a powerful application for the modeling of geometrically complex objects, such as insect wings. The use of the burning algorithm (BA) in digital image processing (DIP) enabled our method to automatically detect an arbitrary domain and its subdomains in a given image. This algorithm, in combination with the mesh generator Distmesh2D, was used to develop detailed FE models of both planar and out-of-plane (i.e., three-dimensionally corrugated) domains containing discontinuities and consisting of numerous subdomains. To easily implement the method, we developed an application using the Matlab App Designer. This application, called WingMesh, was particularly designed and applied for rapid numerical modeling of complicated insect wings but is also applicable for modeling purposes in the earth, engineering, mathematical, and physical sciences.

Functional significance of graded properties of insect cuticle supported by an evolutionary analysis

The exoskeleton of nearly all insects consists of a flexible core and a stiff shell. The transition between these two is often characterized by a gradual change in the stiffness. However, the functional significance of this stiffness gradient is unknown. Here by combining finite-element analysis and multi-objective optimization, we simulated the mechanical response of about 3000 unique gradients of the elastic modulus to normal contacts. We showed that materials with exponential gradients of the elastic modulus could achieve an optimal balance between the load-bearing capacity and resilience. This is very similar to the elastic modulus gradient observed in insect cuticle and, therefore, suggests cuticle adaptations to applied mechanical stresses; this is likely to facilitate the function of insect cuticle as a protective barrier. Our results further indicate that the relative thickness of compositionally different regions in insect cuticle is similar to the optimal estimation. We expect our findings to inform the design of engineered materials with improved mechanical performance.

Biomechanical strategies underlying the durability of a wing-to-wing coupling mechanism

Insects thrived soon after they acquired the ability to fly. Beyond the reach of the non-flying competitors, flying insects colonized a wide variety of habitats. Although flight is an efficient way to disperse and escape predators, it is energetically costly. Hence, various strategies are served to enhance flight efficiency as much as possible. A striking example is the development of wing-to-wing coupling mechanisms in many neopterous insects to minimize the aerodynamic interference of fore and hind wings. However, it remains unclear how the seemingly delicate coupling mechanisms can withstand excessive mechanical stresses encountered during flight. Here we studied the complicated coupling mechanism of drone honey bees, which consists of a set of tiny hooks and a thickened membrane. We found that the durability of the coupling mechanism results from two complementary strategies. First, the angles at which hooks and membrane are coupled and uncoupled may be adjusted, so that the resulting stresses are minimized. Second, the out-of-plane structure, soft base and pronounced tip reduce the stress developed in the hooks, yet maintaining the coupling strength. We anticipate our study, which presents the first numerical model of insect wing coupling mechanisms, to be a starting point for the development of more sophisticated models in the future. Such models are particularly useful for comparative analysis of the influence of different morphological features on the functionality of complex coupling mechanisms. STATEMENT OF SIGNIFICANCE: Hamuli, or 'tiny hooks', is the Greek term for hook-like structures on the anterior margin of honey bee hind wings. By fitting into the fold posterior margin of fore wings, the hooks couple the two wings to each other. Despite their seemingly fragile structure, the hooks withstand substantial mechanical stresses. We show that the out-of-plane structure, soft base and pronounced tip are morphological features that enhance the durability of the hooks, without compromising their function.

A simple, high-resolution, non-destructive method for determining the spatial gradient of the elastic modulus of insect cuticle

Nature has evolved structures with high load-carrying capacity and long-term durability. The principles underlying the functionality of such structures, if studied systematically, can inspire the design of more efficient engineering systems. An important step in this process is to characterize the material properties of the structure under investigation. However, direct mechanical measurements on small complex-shaped biological samples involve numerous technical challenges. To overcome these challenges, we developed a method for estimation of the elastic modulus of insect cuticle, the second most abundant biological composite in nature, through simple light microscopy. In brief, we established a quantitative link between the autofluorescence of different constituent materials of insect cuticle, and the resulting mechanical properties. This approach was verified using data on cuticular structures of three different insect species. The method presented in this study allows three-dimensional visualisation of the elastic modulus, which is impossible with any other available technique. This is especially important for precise finite-element modelling of cuticle, which is known to have spatially graded properties. Considering the simplicity, ease of implementation and high-resolution of the results, our method is a crucial step towards a better understanding of material-function relationships in insect cuticle, and can potentially be adapted for other graded biological materials.

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.

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.

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.

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).

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.

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.

A comparative study of the effects of vein-joints on the mechanical behaviour of insect wings: I. Single joints

The flight performance of insects is strongly affected by the deformation of the wing during a stroke cycle. Many insects therefore use both active and passive mechanisms to control the deformation of their wings in flight. Several studies have focused on the wing kinematics, and plenty is known about the mechanism of their passive deformability. However, given the small size of the vein-joints, accurate direct mechanical experiments are almost impossible to perform. We therefore developed numerical models to perform a comparative and comprehensive investigation of the mechanical behaviour of the vein-joints under external loading conditions. The results illustrate the effect of the geometry and the presence of the rubberlike protein resilin on the flexibility of the joints. Our simulations further show the contribution of the spikes to the anisotropic flexural stiffness in the dorsal and ventral directions. In addition, our results show that the cross veins, only in one joint type, help to transfer the stress to the thicker longitudinal veins. The deformation pattern and the stress distribution in each vein-joint are discussed in detail. This study provides a strong background for further realistic modelling of the dragonfly wing deformation.

Experimental analysis and numerical modeling of mollusk shells as a three dimensional integrated volume

In this paper, a new numerical technique is presented to accurately model the geometrical and mechanical features of mollusk shells as a three dimensional (3D) integrated volume. For this purpose, the Newton method is used to solve the nonlinear equations of shell surfaces. The points of intersection on the shell surface are identified and the extra interior parts are removed. Meshing process is accomplished with respect to the coordinate of each point of intersection. The final 3D generated mesh models perfectly describe the spatial configuration of the mollusk shells. Moreover, the computational model perfectly matches with the actual interior geometry of the shells as well as their exterior architecture. The direct generation technique is employed to generate a 3D finite element (FE) model in ANSYS 11. X-ray images are taken to show the close similarity of the interior geometry of the models and the actual samples. A scanning electron microscope (SEM) is used to provide information on the microstructure of the shells. In addition, a set of compression tests were performed on gastropod shell specimens to obtain their ultimate compressive strength. A close agreement between experimental data and the relevant numerical results is demonstrated.