A hybrid Johnson-Cook and zero-thickness cohesive framework for simulating femoral fracture under ballistic impact

Current research on human cortical bone predominantly focuses on quasi-static or low-velocity impacts, whereas the dynamic response of the femur under extreme ballistic loading remains insufficiently understood. This limitation is largely due to the lack of numerical frameworks capable of simultaneously capturing strain-rate-dependent plasticity and progressive fracture. To address this gap, this study proposes a hybrid finite element framework that combines the Johnson-Cook (J-C) constitutive model with zero-thickness cohesive elements to simulate 9 mm projectile impacts on a three-dimensional anatomical femur model. The J-C model was used to represent the strain-rate hardening and viscoplastic response of the cortical bone matrix, while the cohesive interfaces, governed by a traction-separation law, were employed to simulate crack initiation and propagation. The proposed model reproduced the main macroscopic fracture features observed in experiments, including radiating macro-cracks, transverse fractures, and extensive posterior spalling. Quantitatively, the predicted energy dissipation was approximately 54.5% higher than the experimental mean, which may be attributed to the use of quasi-static cohesive parameters under ultra-high-strain-rate loading and to demographic differences in bone quality. Overall, this hybrid approach provides a useful numerical basis for investigating ballistic femoral fracture mechanics and may support forensic analysis and clinical trauma assessment.