International Journal of Fracture

, Volume 212, Issue 1, pp 105–112 | Cite as

Applicability of hierarchical fiber bundle materials to mechanical environments

  • X. L. Ji
  • L. X. LiEmail author
Brief Note


Biomaterials use a hierarchical structure to optimize their self-healing behavior, for instance. However, the behavior may be constrained under different mechanical environments. In this paper, a system is suggested that the mechanical environment is modeled as a spring connected in series with the fiber bundle material. For the spring, the elastic behavior with stiffness is obeyed while, for the fiber bundle material, the nonlinear elastic constitutive relation is obeyed according to the Weibull distribution and the Daniels’ theory. Relying on the principle of total potential, the applicability condition is proposed for the system and the critical stiffness is thus derived for the spring. The applicability of hierarchical fiber bundle materials is finally investigated. The results show that the hierarchy can significantly change the critical stiffness, and hence demonstrates quite different applicability to a given mechanical environment.


Mechanical environment Hierarchical fiber bundle material (FBM) Spring-FBM in-series system Applicability Critical stiffness 



This work was supported by the National Natural Science Foundation of China (Grant Nos. 11672221, 11272245).


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Key Laboratory for Strength and Vibration of Mechanical Structures, Shaanxi Key Laboratory of Environment and Control for Flight Vehicle, School of AerospaceXi’an Jiaotong UniversityXi’anPeople’s Republic of China

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