title: A numerical study on indentation properties of cortical bone tissue: influence of anisotropy.
abstract: OBJECTIVE
  The purpose of this study is to investigate the effect of anisotropy of cortical bone tissue on measurement of properties such as direction-dependent moduli and hardness.
  
  
  METHODS
  An advanced three-dimensional finite element model of microindentation was developed. Different modelling schemes were considered to account for anisotropy of elastic or/and plastic regimes. The elastic anisotropic behaviour was modelled employing an elasticity tensor, and Hill's criteria were used to represent the direction-dependent post-yield behaviour. The Oliver-Pharr method was used in the data analysis.
  
  
  RESULTS
  A decrease in the value of the transverse elasticity modulus resulted in the increased material's indentation modulus measured in the longitudinal direction and a decreased one in the transverse direction, while they were insensitive to the anisotropy in post-elastic regime. On the other hand, an increase in plastic anisotropy led to a decrease in measured hardness for both directions, but by a larger amount in the transverse one. The size effect phenomenon was found to be also sensitive to anisotropy.
  
  
  CONCLUSIONS
  The undertaken analysis suggests that the Oliver-Pharr method is a useful tool for first-order approximations in the analysis of mechanical properties of anisotropic materials similar to cortical bone, but not necessarily for the materials with low hardening reserves in the plastic regime.
authors.affiliation: Department of Mechanical Engineering, University of Turkish Aeronautical Association, 06790 Ankara, Turkey.
authors.forename: Murat
authors.initials: M
authors.lastname: Demiral
authors.affiliation: Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, LE11 3TU, UK.
authors.forename: Adel
authors.initials: A
authors.lastname: Abdel-Wahab
authors.affiliation: Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, LE11 3TU, UK.
authors.forename: Vadim
authors.initials: V
authors.lastname: Silberschmidt
mesh_terms: D016880:Anisotropy; D001842:Bone and Bones / Q000502:physiology*; D019245:Compressive Strength / Q000502:physiology; D003198:Computer Simulation; D055119:Elastic Modulus / Q000502:physiology*; D020342:Finite Element Analysis; D006244:Hardness / Q000502:physiology*; D006245:Hardness Tests / Q000379:methods; D006801:Humans; D008954:Models, Biological; D013314:Stress, Mechanical