Crack Nucleation & Propagation
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Two-field H design: We separate the strain energy history into two independent fields:
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H_historyย (tight spherical seed) โ feeds the AT2 phase-field PDE solver for localized damage
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H_gradientย (vertical gradient: strong at bottom, zero at mid-height) โ provides a smooth โH for crack tip direction, ensuring consistent bottomโtop propagation
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Radial surface paths: At impact, 6 crack paths are seeded radially outward from the contact center (star pattern), with a low Z-component (z = 0.15) to keep paths near the bottom surface for immediate visibility
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AT2 phase-field PDE: Variational damage model solved via Jacobi iteration. H_crack (5ร H_ref) is seeded along existing crack paths as a boundary condition
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H-gated tip advancement: Tips only advance where local H exceeds 0.1ร H_ref, preventing blind extension into undamaged regions (ears, nose)
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EMA direction smoothingย (ฮฑ = 0.15): Maintains radial propagation direction, gradually rotating upward following โH
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Physics H suppression: MPM stress-driven H is suppressed for 20 frames post-impact, preventing stress wave artifacts at thin geometry (ears, neck). Only the impact-seeded H drives initial crack formation
Rendering
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Gaussian Splatting with crack-aware visualization
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Damaged Gaussians: opacity reduced to 40%, displaced up to 0.004 world units perpendicular to crack surface
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Crack gap fraction: 0.25 for visible splitting effect
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Crack lines rendered as thin geometric damage (width = 0.006) from polyline proximity
