Application of the Johnson-Cook plasticity model in the Finite Element simulations of the nanoindentation of the cortical bone

  • Remache Djamel
  • Semaan Marie
  • Rossi Jean-Marie
  • Pithioux Martine
  • Milan Jean-Louis

  • Mechanical cortical bone behavior
  • Nanoindentation test
  • Inverse optimization approach
  • Design of experiments DOE
  • Johnson-Cook model


The mechanical behavior of the cortical bone in nanoindentation is a complicated mechanical problem. The finite element analysis has commonly been assumed to be the most appropriate approach to this issue. One significant problem in nanoindentation modeling of the elastic-plastic materials is pileup deformation, which is not observed in cortical bone nanoindentation testing. This phenomenon depends on the work-hardening of materials; it doesn't occur for work-hardening materials, which suggests that the cor-tical bone could be considered as a work-hardening material. Furthermore, in a recent study [59], a plastic hardening until failure was observed on the micro-scale of a dry ovine osteonal bone samples subjected to micropillar compression. The purpose of the current study was to apply an isotropic hardening model in the finite element simulations of the nanoindentation of the cortical bone to predict its mechanical behavior. The Johnson-Cook (JC) model was chosen as the constitutive model. The finite element modeling in combination with numerical optimization was used to identify the unknown material constants and then the finite element solutions were compared to the experimental results. A good agreement of the numerical curves with the target loading curves was found and no pileup was predicted. A Design Of Experiments (DOE) approach was performed to evaluate the linear effects of the material constants on the mechanical response of the material. The strain hardening modulus and the strain hardening exponent were the most influential parameters. While a positive effect was noticed with the Young's modulus, the initial yield stress and the strain hardening modulus, an opposite 1 effect was found with the Poisson's ratio and the strain hardening exponent. Finally, the JC model showed a good capability to describe the elastoplastic behavior of the cortical bone.