forked from 1b-agent/fieldcraft-upstream
jyvikoandClaude Opus 5.5
a30d0b5c5b
Segment-to-segment penalty contact between element faces: each secondary face and each main face facing it are projected onto the secondary face's plane, split into triangles, clipped (Sutherland–Hodgman) and integrated with a three-point rule per sub-triangle (Puso–Laursen segmentation, the penalty at the integration points as Fischer–Wriggers), so a uniform pressure gives the consistent nodal forces on both meshes and the contact patch test passes on non-matching meshes. Every contact runs both ways at half the penalty: pairs with each surface as the secondary, general and self contact face against face. A bucket grid of face boxes every increment, faces integrated in parallel and their forces added in face order: the same numbers on any thread count. The penalty per area ε = s γ min(m/A)/Δt² comes from the lumped masses, each node's directional area and the stable increment, bounded by Gershgorin's row sums so contact never shortens the increment. Coulomb friction with exponential decay by a regularised return map at the secondary nodes; rigid walls take Coulomb impulses. Contact work and friction dissipation join the energy balance; each contact reports its peak force, first and last contact, deepest penetration, friction and the nodes adjusted at the start (initial penetrations adjusted strain-free or refused with the node, face and depth); a cap on contact faces. Verified (crates/explicit/tests/contact.rs, tests/oracle/explicit-*): colliding bars (2L/c +1.2%, ρcAv₀/2, KE kept to 0.005%, contact energy back to 8e-5 of it), blocks sliding to a stop on a rigid wall and on a plate under constant and decaying friction (0.005–0.2%), the patch test (σ_zz uniform to 0.06%), two spheres colliding against Hertz (peak +2.3%, duration −0.4%; the oracle case waits for a graded sphere mesher), a free body untouched by general contact, determinism across threads. Oracle measures gain `over` (ratios). Existing fixtures do not move. Co-Authored-By: Claude Opus 5.5 <[email protected]> Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm
9 lines
643 B
Markdown
9 lines
643 B
Markdown
# Two elastic spheres colliding head-on (explicit contact, Hertz)
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Two identical steel spheres, R = 10 mm, E = 210 GPa, ν = 0.3, ρ = 7.85 t/m³ (mm, t, s, N, MPa),
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meet head-on at a relative speed of 1 m/s. Hertz's quasi-static theory gives the approach
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δ = 0.020441 mm, the contact radius a = √(R* δ) = 0.320 mm, the peak force 1005.4 N and the
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contact duration 60.16 μs. The case waits for a graded sphere mesh built from commands: the contact
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radius is a thirtieth of the sphere's, so the mesh must be fine at the poles and coarse elsewhere.
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The explicit crate's tests check the same theory on a cubed-sphere mesh generated in code.
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