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.
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.
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.
Although wings of insects show a large variation in morphology, they are all made from a network of irregular veins interconnected through membranous areas. Depending on their shape, size, and position, wing veins are usually divided into three different groups: longitudinal veins, cross-veins and ambient veins. The veins together with the membrane and some other elements such as spines, nodus and pterostigma can be considered as the wing’s “constructional elements”. In spite of rather extensive literature on dragonfly wing structure, the role of each of these elements in determining the wing’s function remains mostly unknown. As this question is difficult to answer in vivo using biomechanical experiments on actual wings, this study was undertaken to reveal the effects of the constructional elements on the mechanical behaviour of dragonfly wings by applying numerical simulations. An image processing technique was used to develop 12 finite element models of the insect wings with different constructional elements. The mechanical behaviour of these models was then simulated under normal and shear stresses due to tension, bending and torsion. A free vibration analysis was also performed to determine the resonant frequencies and the mode shapes of the models. For the first time, a quantitative comparison was carried out between the mechanical effects selectively caused by different elements. Our results suggest that the complex interactions of veins, membranes and corrugations may considerably affect the dynamic deformation of the insect wings during flight
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