Predicting Fracture Load and Trajectory in Long Bones by Phase Field Models
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Patient-specific CT-based finite element analysis (FEA) of human bones may aid clinicians in estimating the risk of bone fracture [1]. In these FEAs the heterogeneous distribution of bone ash density (ρash) is correlated to the heterogeneous Young’s modulus of the bone tissue. However, predicting fracture initiation and crack trajectories by applying phase field models requires the heterogeneous fracture toughness GIc and critical strain c that may be determined by different experimental methods. An experimental campaign was undertaken on cortical specimens from two fresh frozen femurs to determine the heterogeneous fracture toughness GIc and the critical strain Ec, shown to be independent of the density. The heterogeneous fracture toughness perpendicular to osteons’ direction was found to be [2]: GIc[N/m] = 321.94 (ρash[gr/cc])^1.69 and the critical tensile strain resulting in a nonlinear response [3]: Ec= 7300 μstrain We use these values to investigate the predictability of a FE-PF model when applied to long bones for estimating the risk of hip and proximal humeral fractures. REFERENCES [1] Z. Yosibash Z., Y. Katz, N. Trabelsi A. and Sternheim, ``Femurs segmentation by machine learning from CT scans combined with autonomous finite elements in orthopedic and endocrinology applications'', Comp. Math. Appl., 152, pp. 1 – 27, (2023) [2] M. Levy and Z. Yosibash Z., ``Heterogeneous Fracture Toughness of Human Cortical Bone Tissue'', Int. Jour. Fracture, 249, article 17, (2025) [3] M. Levy and Z. Yosibash Z., ``Fracture Initiation in Heterogeneous Human Cortical Bone Tissues Predicted by PFM'', Submitted for publication (2026)
