Numerical investigation of the material gradient using different stiffness functions by consideration of the graded stiffness of the dragonfly wing membrane

Most natural materials are composites that can exhibit a wide range of material properties, such as the elastic modulus. Insect cuticle is one of these natural materials. The material gradient of the cuticle drastically varies in different insect body parts. Considering the small size of cuticular samples, conducting experimental tests is very challenging, expensive, and time-consuming. Understanding how cuticular structures work and their graded properties can help to design and develop engineering materials with enhanced properties. In this paper, the finite element (FE) method is used to investigate the function of the cuticle in the membrane of dragonfly wings. In this regard, first, the distribution of materials on the wing membrane is investigated using images obtained by confocal laser scanning microscope (CLSM). Then, in order to estimate the stress and strain values subjected to displacement, multiple stiffness functions are applied for a geometric model of a cantilever beam, which represents the membrane. The results show that the presence of a graded stiffness has a significant effect on the mechanical behavior of the cantilever beam. A comparison of the results obtained from the analysis of different stiffness functions showed that The quadratic function is introduced as a more suitable distribution for stiffness, in terms of having the least stress and strain in this structure, compared to other stiffness functions. This study can provide a proper and applied platform for further interdisciplinary research in this area.