Acta Mechanica Solida Sinica

, Volume 20, Issue 3, pp 198–205 | Cite as

Effective elastic modulus of bone-like hierarchical materials

  • Shuchun Zuo
  • Yueguang Wei


A shear-lag model is used to study the mechanical properties of bone-like hierarchical materials. The relationship between the overall effective modulus and the number of hierarchy level is obtained. The result is compared with that based on the tension-shear chain model and finite element simulation, respectively. It is shown that all three models can be used to describe the mechanical behavior of the hierarchical material when the number of hierarchy levels is small. By increasing the number of hierarchy level, the shear-lag result is consistent with the finite element result. However the tension-shear chain model leads to an opposite trend. The transition point position depends on the fraction of hard phase, aspect ratio and modulus ratio of hard phase to soft phase. Further discussion is performed on the flaw tolerance size and strength of hierarchical materials based on the shear-lag analysis.

Key words

hierarchical materials tension-shear chain model shear-lag model 


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2007

Authors and Affiliations

  • Shuchun Zuo
    • 1
  • Yueguang Wei
    • 1
  1. 1.LNMInstitute of Mechanics, Chinese Academy of SciencesBeijingChina

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