COMPLAS 2023

Characterizing The Elasto-Plastic Anisotropic Mechanical Property Of Cancellous Bone Via a Baysian Calibration Method

  • Yan, Ziming (Tsinghua University)
  • Liu, Zhanli (Tsinghua University)
  • Zhuang, Zhuo (Tsinghua University)

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Mechanical properties of cancellous bone are heterogeneous and anisotropic due to the differences of regional microstructure. Traditional experimental tests for characterizing bone's mechanical properties usually hypothesize a uniaxial stress condition without quantitatively evaluating the influence of spatially varying principal material orientations, which cannot accurately predict the mechanical properties distribution of bones in vivo environment. In this study, A constitutive model considering heterogeneity is developed to describe the elasto-plastic mechanical behavior of cancellous. A Bayesian calibrating procedure based on the three-dimension direct problem model was developed using quantified multiaxial stress to investigate cancellous bone's local anisotropic elasto-plastic performance around joints as the spatial variation of main bearing orientations. The multiaxial stress state of each bone specimen is calibrated using the actual principal material orientations derived from fabric tensor at different anatomical locations. Based on the calibrated multiaxial stress state, the process of identifying mechanical properties is described as an inverse problem. Then, a Bayesian calibration procedure based on a surrogate constitutive model was developed via multiaxial stress correction to identify the anisotropic material parameters. Finally, a comparison between the experiment and simulation results is discussed by applying the optimal model parameters obtained from the Bayesian probability distribution. Compared to traditional uniaxial methods, our results prove that the calibration based on the spatial variation of the main bearing orientations can significantly improve the accuracy of characterizing regional anisotropic mechanical responses. Moreover, we determine that the actual mechanical property distribution is influenced by complicated mechanical stimulation. This study provides a novel method to evaluate the spatially varying mechanical properties of bone tissues enduring complex mechanical loading.