PSI - Issue 77

Zihao Liu et al. / Procedia Structural Integrity 77 (2026) 190–197 Z. Liu et al./ Structural Integrity Procedia 00 (2026) 000–000

192

3

Various loading conditions are compared in this study with an aim to investigate the adaptation mechanisms of representative bone elements with different initial geometries. The workflow of generation of initial bone morphology setup and adjusting the element size is implemented with Python scripts. 2.1 FE model setup Two initial morphologies of TB were examined in this research (Fig. 1), using shapes of X and Z letters. The former shape is a minimal model of two intersecting trabeculae, compatible with the rod-and-plate trabecular segmentation frameworks. It has the potential to develop into various geometries. On the other hand, the morphology evolution of the Z shape introduces the geometric asymmetry of the trabeculae, providing insights into directional sensitivity of TBA.

Fig. 1. Initial morphology and boundary conditions of FEA models The boundary conditions of the mechanical BA model are illustrated in Figure 1. The representative volume element (RVE) had the size of 1000 μ m x 400 μ m x 700 μ m . The top and bottom faces of the RVE are tied to the rigid plates to transfer the applied load to the studied domain. The bottom rigid plate was fully fixed, with the pressure of 2 MPa applied to the top rigid plate. 2.2 Model for bone adaptation 2.2.1 Mathematical model for bone adaptation with stimulus non-uniformity The developed models simulated osteocyte sensing as a distance-weighted contributions, between the local signal at the bone surface site and the weighted surface-bone signals within the mechanosensory range 0 . In the SED-based TBA model, where stands for SED at element , the mechanical signal is express as = = 2 (1) In Eq. (1), the mechanical signal at element is the elastic strain-energy density. In the TBA model based on von Mises stress, where is a scalar von Mises stress measure, the mechanical signal is as follows: = (2) To get a weighted contribution from neighbours within the mechanosensory range 0 , a linear decay function ( ) is used: ( ) =1 − 0 , 0 ≤ 0 (3)

Information classification: Internal