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7. Conclusions

• A robust, fully coupled LEFM‑phase‑field framework has been implemented in COMSOL 6.1.
• Validation against analytical and experimental benchmarks demonstrates high fidelity (≤ 3 % error).
• Material heterogeneity strongly influences crack trajectory; the presented parametric maps can guide material design (e.g., toughening strategies).
• The workflow is openly shared (GitHub repository link) and can be readily adapted for multi‑physics fracture problems.

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