The emergence of an unusual stiffness profile in hierarchical biological tissues

Benny Bar-On, H. Daniel Wagner

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Biological tissues usually exhibit complex multiscale structural architectures. In many of these, and particularly in mineralized tissues, the basic building block is a staggered array-a composite material made of soft matrix and stiff reinforcing elements. Here we study the stiffness of non-overlapping staggered arrays, a case that has not previously been considered in the literature, and introduce closed-form analytical expressions for its Young's modulus. These expressions are then used to estimate the stiffness of natural staggered biocomposites such as low-mineralized collagen fibril and mineralized tendon. We then consider a two-scale composite scheme for evaluating the modulus of a specific hierarchical structure, the compact bone tissue, which is made of mineralized collagen fibrils with weakly overlapping staggered architecture. It is found that small variations in the staggered structure induce significant differences in the macroscopic stiffness, and, in particular, provide a possible explanation for the as yet unexplained stiffening effects observed in medium-mineralized tissues.

Original languageEnglish
Pages (from-to)8099-8109
Number of pages11
JournalActa Biomaterialia
Issue number9
StatePublished - 1 Jan 2013
Externally publishedYes


  • Biological composites
  • Bone mechanics
  • Multi-scale bio-materials
  • Staggered structure

ASJC Scopus subject areas

  • Biotechnology
  • Biomaterials
  • Biochemistry
  • Biomedical Engineering
  • Molecular Biology


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