Analytical Expression for the J-Integral in Ramberg-Osgood Materials via Symbolic Regression

We present a mechanics-informed, model-free symbolic regression framework to derive analytical expressions for the J-integral in elastic-plastic fracture mechanics. Building on our prior work in linear elastic fracture mechanics, we extend the method to metallic materials using data-driven variable separation and dimensional analysis. The resulting expression accurately captures the nonlinear fracture response of single-edge notched beam (SENB) specimens, exhibiting good generalizability. This framework offers an engineer-friendly tool for rapid fracture assessment in aerospace structures and materials.