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.