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| Parameter | Range | Observations | |-----------|-------|--------------| | Elastic modulus contrast (E_\texthard/E_\textsoft) | 1 – 10 | Higher contrast → increased stress concentration at interfaces, earlier crack branching. | | Fracture toughness gradient (\nabla G_c) | 0 – 0.5 MPa·m(^1/2)/mm | Positive gradient (tougher ahead) deflects crack toward softer side; negative gradient accelerates straight propagation. | | Phase‑field regularization length (\ell) | 0.1 – 2 mm | Larger (\ell) smooths crack path, reduces mesh sensitivity, but over‑diffuses sharp kinks. Recommended (\ell \approx 3–5) element sizes. |

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