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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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COMSOL 6.1 is a powerful multiphysics simulation software that offers a wide range of features and tools to help users optimize their designs and improve performance. While downloading the crack version may seem appealing, please ensure you comply with software policies and regulations. By leveraging the capabilities of COMSOL 6.1, users can increase productivity, reduce costs, and improve product performance.