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Material model of pelvic bone based on modal analysis: a study on the composite bone


Digital models based on finite element (FE) analysis are widely used in orthopaedics to predict the stress or strain in the bone due to bone–implant interaction. The usability of the model depends strongly on the bone material description. The material model that is most commonly used is based on a constant Young’s modulus or on the apparent density of bone obtained from computer tomography (CT) data. The Young’s modulus of bone is described in many experimental works with large variations in the results. The concept of measuring and validating the material model of the pelvic bone based on modal analysis is introduced in this pilot study. The modal frequencies, damping, and shapes of the composite bone were measured precisely by an impact hammer at 239 points. An FE model was built using the data pertaining to the geometry and apparent density obtained from the CT of the composite bone. The isotropic homogeneous Young’s modulus and Poisson’s ratio of the cortical and trabecular bone were estimated from the optimisation procedure including Gaussian statistical properties. The performance of the updated model was investigated through the sensitivity analysis of the natural frequencies with respect to the material parameters. The maximal error between the numerical and experimental natural frequencies of the bone reached 1.74 % in the first modal shape. Finally, the optimised parameters were matched with the data sheets of the composite bone. The maximal difference between the calibrated material properties and that obtained from the data sheet was 34 %. The optimisation scheme of the FE model based on the modal analysis data provides extremely useful calibration of the FE models with the uncertainty bounds and without the influence of the boundary conditions.

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This publication was written at the Technical University of Liberec, Faculty of Mechanical Engineering with the support of the Institutional Endowment for the Long Term Conceptual Development of Research Institutes, as provided by the Ministry of Education, Youth and Sports of the Czech Republic in the year 2016.

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Correspondence to Petr Henyš.

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Henyš, P., Čapek, L. Material model of pelvic bone based on modal analysis: a study on the composite bone. Biomech Model Mechanobiol 16, 363–373 (2017).

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  • Modal analysis
  • Pelvic bone
  • Finite element
  • Optimisation
  • Uncertainty