Multiscale Modeling for Mechanical Properties of Cancellous Bone Based on the Schwarz Surface

Microstructure and the mechanical properties of cancellous bone were modeled by multiscale finite element method in this paper. Microstructure of the cancellous bone determines its mechanical properties and a rational geometry modeling of the cancellous bone is fundamental to predict the material properties. In this paper, we generate a new parameterized microstructural unit cell model based on triple periodic minimal surfaces (TPMS) which is established by the Schwarz surface with various volume fractions. This model truly simulates the microstructure of the cancellous bone and satisfies some biological and mechanical requirements. By using the new unit cell model, the second-order two-scale (SOTS) method is applied to predict the mechanical properties of cancellous bone. The predictive the mechanical properties of numerical results are in good agreement with the experimental data reported in literature, which demonstrate that the established unit cell model is applicable and the second-order two-scale method is valid to predict the mechanical properties of cancellous bone.