I'm currently working on modeling the Wöhler (S-N) curve analytically, but the results I'm getting are not aligning well with my experimental fatigue data. I've tried several classical approaches (e.g., Basquin’s law, Coffin-Manson), but the discrepancies remain significant.

I'm looking for:

• Recommendations on reliable analytical or semi-analytical methods for constructing the S-N curve.
• Any guidance on incorporating material parameters or microstructural effects analytically.
• Examples or references where the analytical Wöhler curve has shown good agreement with experimental results.

Are there improved models or modifications that better reflect the fatigue behavior under cyclic loading, especially for metals or composites?

Any shared experiences, datasets, or references would be greatly appreciated.