Hierarchical modeling of elastic moduli of equine hoof wall

Cheng Shen (Andrew) Shiang, Christian Bonney, Benjamin Lazarus, Marc Meyers, Iwona Jasiuk

Research output: Contribution to journalArticlepeer-review


This study predicts analytically effective elastic moduli of substructures within an equine hoof wall. The hoof wall is represented as a composite material with a hierarchical structure comprised of a sequence of length scales. A bottom-up approach is employed. Thus, the outputs from a lower spatial scale serve as the inputs for the following scale. The models include the Halpin-Tsai model, composite cylinders model, a sutured interface model, and classical laminate theory. The length scales span macroscale, mesoscale, sub-mesoscale, microscale, sub-microscale, and nanoscale. The macroscale represents the hoof wall, consisting of tubules within a matrix at the mesoscale. At the sub-mesoscale, a single hollow tubule is reinforced by a tubule wall made of lamellae; the surrounding intertubular material also has a lamellar structure. The lamellae contain sutured and layered cells at the microscale. A single cell is made of crystalline macrofibrils arranged in an amorphous matrix at the sub-microscale. A macrofibril contains aligned crystalline rod-like intermediate filaments at the nanoscale. Experimentally obtained parameters are used in the modeling as inputs for geometry and nanoscale properties. The predicted properties of the hoof wall material agree with experimental measurements at the mesoscale and macroscale. We observe that the hierarchical structure of the hoof wall leads to a decrease in the elastic modulus with increasing scale, from the nanoscale to the macroscale. Such behavior is an intrinsic characteristic of hierarchical biological materials. This study can serve as a framework for designing impact-resistant hoof-inspired materials and structures.

Original languageEnglish (US)
Article number105529
JournalJournal of the Mechanical Behavior of Biomedical Materials
StatePublished - Dec 2022
Externally publishedYes


  • Elastic moduli
  • Equine hoof wall
  • Keratin
  • Modeling
  • Structural hierarchy

ASJC Scopus subject areas

  • Mechanics of Materials
  • Biomedical Engineering
  • Biomaterials


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