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.
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The authors would like to thank Mr. Ali Shafiei (McGill University) for his helpful comments during the finite element modelling. Funding This study was financially supported by “Federal State Funding at Kiel University” to HR. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.
H.R., A.D., S.N.G., D.T. and J-H.D. designed and coordinated the study; S.E. performed the image processing analysis; H.R., P.B. and A.P. conducted the computational analysis and analysed the data; H.R. wrote the manuscript; all the authors reviewed the manuscript, discussed the results and gave the final approval for publication.
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The authors declare there are no competing interests to disclose.
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Rajabi, H., Bazargan, P., Pourbabaei, A. et al. Wing cross veins: an efficient biomechanical strategy to mitigate fatigue failure of insect cuticle. Biomech Model Mechanobiol 16, 1947–1955 (2017). https://doi.org/10.1007/s10237-017-0930-6
- Crack propagation
- Finite element