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.