A method of numerical homogenization of inhomogeneous porous medium elements based on digital prototype data

The relevant problem of bone biomechanics is the determination of averaged mechanical properties, which makes it possible to scale computational models and use the data obtained to calculate full-size samples of heterogeneous structure. The article considers a CT-based method for numerical homogenization of an inhomogeneous porous medium. The approach is based on the averaging of RVE mechanical properties corresponding to the heterogeneity characteristic size. Additively made cubes with heterogeneity in the ellipsoid form with a small semi-axis directed at three specified angles were considered for the validation. The influence of the ellipsoid's directivity was also studied based on full-scale experiments, assuming that the empty area was filled with low stiffness air. The bone trabecular structure elements extracted from X-ray CT-images of the bone organs of dwarf pigs were used as model samples: the experimental groups corresponded to different morphological parameters of bone tissue. The work involved validating a new approach to determining averaged mechanical properties by comparing them with data from full-scale experiments, as well as conducting a comparative analysis of the method accuracy and computational efficiency relative to existing analogues in calculating complex structural biological samples based on digital prototypes. The results obtained showed compliance with full-scale test data, a weak effect of structural heterogeneity on the surface of boundary conditions, as well as high simulation speed in calculations based on high-resolution medical images. Thus, the implemented numerical-digital approach makes it possible to average the mechanical properties of heterogeneous porous materials, taking into account their unique distribution.