Analysis of anisotropic viscoelastoplastic properties of cortical bone tissues

Adel A. Abdel-Wahab*, Khurshid Alam, Vadim V. Silberschmidt

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

124 Citations (Scopus)


Bone fractures affect the health of many people and have a significant social and economic effect. Often, bones fracture due to impacts, sudden falls or trauma. In order to numerically model the fracture of a cortical bone tissue caused by an impact it is important to know parameters characterising its viscoelastoplastic behaviour. These parameters should be measured for various orientations in a bone tissue to assess bone's anisotropy linked to its microstructure. So, the first part of this study was focused on quantification of elastic-plastic behaviour of cortical bone using specimens cut along different directions with regard to the bone axis-longitudinal (axial) and transverse. Due to pronounced non-linearity of the elastic-plastic behaviour of the tissue, cyclic loading-unloading uniaxial tension tests were performed to obtain the magnitudes of elastic moduli not only from the initial loading part of the cycle but also from its unloading part. Additional tests were performed with different deformation rates to study the bone's strain-rate sensitivity. The second part of this study covered creep and relaxation properties of cortical bone for two directions and four different anatomical positions-anterior, posterior, medial and lateral-to study the variability of bone's properties. Since viscoelastoplasticity of cortical bone affects its damping properties due to energy dissipation, the Dynamic Mechanical Analysis (DMA) technique was used in the last part of our study to obtain magnitudes of storage and loss moduli for various frequencies. Based on analysis of elastic-plastic behaviour of the bovine cortical bone tissue, it was found that magnitudes of the longitudinal Young's modulus for four cortical positions were in the range of 15-24 GPa, while the transversal modulus was lower - between 10 and 15 GPa. Axial strength for various anatomical positions was also higher than transversal strength with significant differences in magnitudes for those positions. Quantitative data obtained in creep and relaxation tests exhibited no significant position-specific differences. DMA results demonstrated relatively low energy-loss capability due to viscosity of bovine cortical bone that has a loss factor in the range of 0.035-0.1.

Original languageEnglish
Pages (from-to)807-820
Number of pages14
JournalJournal of the Mechanical Behavior of Biomedical Materials
Issue number5
Publication statusPublished - Jul 2011
Externally publishedYes


  • Cortical bone
  • Creep
  • DMA
  • Loss modulus
  • Relaxation
  • Storage modulus
  • Viscoelasticity

ASJC Scopus subject areas

  • Biomaterials
  • Biomedical Engineering
  • Mechanics of Materials


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