Physical deep symbolic regression to learn crack tip correction formulas

This repository publishes the data generated in the article "A universal crack tip correction algorithm discovered by physical deep symbolic regression" (see preprint: arXiv.2403.10320).

This repository is structured with the following subfolders:

01_Simulation_Output: The results of the finite element (FE) simulations described in the paper

02_CrackPy_single_evaluation: For each FE simulation, the fracture analysis results of CrackPy performed with the crack tip as origin

04_CrackPy_random_evaluation_pipeline: For each FE simulation, the fracture analysis is performed at 1000 random perturbations of the crack tip position as origin and the results are stored in the subfolder samples

05_1_PhySO_log_mode_I, 05_2_PhySO_log_mode_II, 05_3_PhySO_log_mixed_mode: These folders contain the logs of three distinct training runs of PhySO - mode I, mode II, and mixed mode. For each of these three load cases, we train symbolic regression models for the x-correction and y-correction separately. The symbolic regression results are stored in the files curves_pareto.csv 

06_Pareto_Plots: The visualization of the Pareto front for each training run of PhySO

07_Plots_vector_fields: The correction vector fields for each discovered Pareto formula

08_Convergence_study_FEA: The iterative convergence behavior for the FE simulations data

13_Application: We applied the most promising formulas to experimental DIC data from uniaxial and biaxial fatigue crack growth experiments. The results are contained in this folder.

The code to reproduce these results can be fould on our GitHub page at the following link: https://github.com/dlr-wf/crack_tip_correction_symbolic_regression