Annals of Biomedical Engineering

, Volume 33, Issue 1, pp 26–38

Hydraulic Strengthening Affects the Stiffness and Strength of Cortical Bone


DOI: 10.1007/s10439-005-8960-0

Cite this article as:
Liebschner, M.A.K. & Keller, T.S. Ann Biomed Eng (2005) 33: 26. doi:10.1007/s10439-005-8960-0


A nonlinear, interstitial fluid flow constitutive model for cortical bone was developed to study the strain-rate dependency of cortical bone apparent modulus (Ea). Nine representative volume element (RVE) structural models of cortical bone spanning an effective pore volume fraction P range of 1–40% were examined. Dynamic loading conditions were used to study the fluid flow contribution or hydraulic strengthening (HS) effect on Ea for each RVE model. The model indicated that there is an upper and lower asymptotic bound of strain-rate (10± 3 sec−1) above or below which there are no further HS effects on Ea. At certain strain-rates (10−1 to 100 sec−1) variations in cortical bone porosity had little or no influence on Ea. At lower and higher frequencies, the loss tangent, hence the magnitude of viscoelastic effects is greater. For strain-rates less than 10−1 sec−1, lower porosity RVE models were always stiffer than higher porosity RVE models. A generalized power law model is proposed to account for the fact that HS in cortical bone exhibits an upper and lower asymptotic bound and is bi-modal in terms of strain-rate.

Fluid flow Bi-phasic model Unit cell analysis Finite element analysis Cortical bone Hydraulic strengthening 

Copyright information

© Biomedical Engineering Society 2005

Authors and Affiliations

  1. 1.Department of BioengineeringRice UniversityHouston
  2. 2.Department of Mechanical EngineeringThe University of VermontBurlington
  3. 3.Department of BioengineeringRice UniversityHouston

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