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
107 lines
3.1 KiB
JSON
107 lines
3.1 KiB
JSON
{
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"title": "Two identical elastic bars colliding (explicit contact)",
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"kind": "theory",
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"source": "One-dimensional elastic impact of equal bars: contact for 2L/c, interface force ρcAv₀/2, exchange of velocities, no loss of energy; Graff, Wave Motion in Elastic Solids, Dover 1991, §2.1–2.3; Johnson, Impact Strength of Materials, Arnold 1972, §1.6",
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"quantities": [
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{
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"id": "duration",
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"quantity": "time of the last contact (the bars touch from t = 0) against 2L/c = 0.2",
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"measure": {
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"from": "solve",
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"pointer": "/contacts/0/last_contact"
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},
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"value": 0.2,
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"tolerance": {
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"relative": 0.02
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},
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"reason": "the penalty springs at the interface delay the release by a few element transit times (about 1% of 2L/c with 200 elements per bar)"
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},
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{
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"id": "force",
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"quantity": "the largest force across the interface against ρcAv₀/2 = 0.05",
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"measure": {
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"from": "solve",
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"pointer": "/contacts/0/peak_force"
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},
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"value": 0.05,
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"tolerance": {
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"relative": 0.04
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},
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"reason": "the plateau is ρcAv₀/2 to 0.01%; the peak is the plateau plus the ringing behind the discrete wave front, a few percent"
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},
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{
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"id": "v_a",
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"quantity": "velocity of the struck bar's far end after the impact (0: the striker stops)",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Impact",
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"at": [
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[
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0,
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0,
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0
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]
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]
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},
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"pointer": "/nodes/0/velocity/0"
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},
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"value": 0.0,
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"tolerance": {
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"absolute": 0.005
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},
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"reason": "the striker stops on average (its kinetic energy is under 0.01% of the start's, see ke); its far end node keeps the ringing of the discrete release front, a few percent of v₀"
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},
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{
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"id": "v_b",
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"quantity": "velocity of the struck bar's far end after the impact (v₀ = 0.1)",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Impact",
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"at": [
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[
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20.0,
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0,
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0
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]
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]
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},
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"pointer": "/nodes/0/velocity/0"
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},
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"value": 0.1,
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"tolerance": {
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"relative": 0.05
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},
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"reason": "the struck bar leaves at v₀ on average; its far end node keeps the ringing of the discrete wave fronts, a few percent"
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},
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{
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"id": "ke",
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"quantity": "kinetic energy after the impact over ½mv₀² (frictionless elastic impact)",
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"measure": {
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"from": "solve",
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"pointer": "/energy/kinetic",
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"scale": 2000.0
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},
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"value": 1.0,
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"tolerance": {
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"relative": 0.01
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},
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"reason": "an elastic impact keeps the kinetic energy; the quadratic bulk viscosity at the compression fronts and the vibration left in the bars take a fraction of a percent"
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},
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{
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"id": "contact_energy",
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"quantity": "energy left in the contact after the separation, over ½mv₀² (its drift)",
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"measure": {
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"from": "solve",
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"pointer": "/energy/contact",
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"scale": 2000.0
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},
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"value": 0.0,
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"tolerance": {
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"absolute": 0.001
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},
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"reason": "the penalty springs give back what they took; the trapezoidal work of a spring that engages between increments drifts by far less than 0.1%"
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}
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]
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} |