Biomechanics and Modeling in Mechanobiology

, Volume 16, Issue 6, pp 1947–1955 | Cite as

Wing cross veins: an efficient biomechanical strategy to mitigate fatigue failure of insect cuticle

  • H. RajabiEmail author
  • P. Bazargan
  • A. Pourbabaei
  • Sh. Eshghi
  • A. Darvizeh
  • S. N. Gorb
  • D. Taylor
  • J.-H. Dirks
Original Paper


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.


Cuticle Fatigue Crack propagation Wing Finite element 



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.

Compliance with ethical standards

Authors’ contributions

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.

Conflict of interest

The authors declare there are no competing interests to disclose.

Supplementary material

10237_2017_930_MOESM1_ESM.mp4 (38.2 mb)
Video S1: Numerical simulation of crack propagation in the locust S. gregaria hindwing under fluctuating stresses. (38.2 MB)


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • H. Rajabi
    • 1
    • 2
    Email author
  • P. Bazargan
    • 2
    • 3
  • A. Pourbabaei
    • 2
    • 4
  • Sh. Eshghi
    • 5
  • A. Darvizeh
    • 6
  • S. N. Gorb
    • 1
  • D. Taylor
    • 7
  • J.-H. Dirks
    • 8
  1. 1.Institute of Zoology, Functional Morphology and BiomechanicsKiel UniversityKielGermany
  2. 2.Department of Mechanical EngineeringUniversity of GuilanRashtIran
  3. 3.Institute of Forming Technology and Lightweight ConstructionTechnical University of DortmundDortmundGermany
  4. 4.Department of Mechanical EngineeringTarbiat Modares UniversityTehranIran
  5. 5.Young Researchers and Elite Club, Lahijan BranchIslamic Azad UniversityLahijanIran
  6. 6.Department of Mechanical Engineering, Bandar Anzali BranchIslamic Azad UniversityBandar AnzaliIran
  7. 7.Trinity Centre for BioengineeringTrinity College DublinDublinIreland
  8. 8.Biomimetics-Innovation-CentreBremen City University of Applied SciencesBremenGermany

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