Geometry-based surrogate modelling for peak stress assessment in flat and cross-curved bone plates subjected to transverse bending

The increasing geometrical complexity of bone plates, driven by the adoption of anatomically precontoured designs to improve fit and biomechanical performance, requires efficient tools for structural evaluation to support implant design. Finite Element (FE) simulations provide accurate stress evaluations but remain computationally demanding when multiple design iterations are required. Moreover, existing analytical approaches for stress concentration factor (SCF) estimation are mainly limited to simplified geometries and do not account for the cross-curvature typical of commercial bone plates. This study develops a geometry-based computational framework for rapid SCF estimation in bone plates subjected to transverse bending under the pure bending condition representative of the ASTM F382-24 four-point bending test. FE simulations were combined with a Design of Experiments (DOE) approach to generate a dataset representative of commercial plate geometries, including thickness, width, hole diameter, and cross-curvature radius. Surrogate polynomial (SP) models were then developed to predict SCFs directly from plate geometry, enabling rapid estimation of peak bending stresses without repeated FE analyses. The developed models were validated on thirteen commercial bone plates excluded from the training dataset by comparing peak bending stresses obtained from SP-predicted SCFs and full FE simulations. The SP models showed strong predictive capability, with coefficients of determination up to R² = 0.95 and most stress prediction errors below 10%. Cross-curvature significantly affected SCF estimation, producing variations up to 18% compared with flat-plate assumptions. This framework provides a rapid computational tool for screening bone plate designs, enabling efficient mechanical assessment of anatomically contoured implants while reducing reliance on time-consuming FE simulations.