forked from 1b-agent/fieldcraft-upstream
jyvikoandClaude Opus 5.5
945a2076c3
Two oracle cases: the contact patch test on non-matching meshes in small and finite sliding, and Hertz's cylinder on a flat under force control (peak pressure, pressure distribution, subsurface stress). docs/fem.md describes the formulation, the literature survey its papers; ROADMAP M7 and parity are updated. Co-Authored-By: Claude Opus 5.5 <[email protected]> Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
109 lines
3.5 KiB
JSON
109 lines
3.5 KiB
JSON
{
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"title": "Hertz line contact: a cylinder pressed on a flat (implicit mortar contact, plane strain)",
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"kind": "theory",
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"source": "H. Hertz, Über die Berührung fester elastischer Körper, J. reine angew. Math. 92:156–171, 1882; K. L. Johnson, Contact Mechanics, Cambridge University Press 1985, §4.3 (two-dimensional contact of cylindrical bodies, eqs. 4.45–4.49): b = √(4PR/(πE*)), p₀ = 2P/(πb), with 1/E* = 2(1 − ν²)/E for two bodies of one material and R the cylinder's radius on a flat",
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"quantities": [
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{
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"id": "peak_pressure",
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"quantity": "the largest contact pressure p₀ (at x = 0)",
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"measure": {
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"from": "solve",
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"pointer": "/contacts/0/max_pressure/value"
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},
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"value": 2884.6153846153843,
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"tolerance": {
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"relative": 0.02
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},
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"reason": "p₀ = 2P/(πb) for the load per length P = 2265.57 N/mm, b = 0.5 mm; the contact width spans seven elements of the graded mesh"
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},
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{
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"id": "normal_force",
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"quantity": "the force across the contact (half model, 1 mm thick)",
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"measure": {
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"from": "solve",
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"pointer": "/contacts/0/normal_force"
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},
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"value": 1132.7858125924733,
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"tolerance": {
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"relative": 0.002
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},
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"reason": "the pressure carries the whole load; the soft springs that hold the indenter before contact take a millionth"
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},
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{
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"id": "pressure_x0296",
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"quantity": "the contact pressure at the secondary node at x = 0.29594 (node 7)",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Press",
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"nodes": [
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7
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]
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},
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"pointer": "/nodes/0/contact/0/pressure"
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},
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"value": 2325.066800691437,
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"tolerance": {
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"relative": 0.05
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},
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"reason": "p₀ √(1 − x²/b²) at the node; the nodal pressure (the node's normal force over the area it carries) averages the distribution over the node's elements"
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},
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{
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"id": "pressure_x0367",
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"quantity": "the contact pressure at the secondary node at x = 0.36701 (node 8)",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Press",
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"nodes": [
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8
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]
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},
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"pointer": "/nodes/0/contact/0/pressure"
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},
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"value": 1959.0164149439815,
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"tolerance": {
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"relative": 0.1
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},
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"reason": "as at node 7, nearer the edge, where the elements round off the square-root fall of the pressure to zero at b"
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},
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{
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"id": "pressure_x0633",
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"quantity": "the contact pressure at the secondary node at x = 0.63325 (node 11, beyond the half-width b = 0.5)",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Press",
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"nodes": [
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11
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]
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},
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"pointer": "/nodes/0/contact/0/pressure"
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},
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"value": 0.0,
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"tolerance": {
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"absolute": 1.0
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},
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"reason": "outside the contact the surfaces are apart: no pressure (an element beyond b, since the edge element carries part of the last closed node's pressure)"
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},
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{
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"id": "syy_depth",
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"quantity": "the vertical stress σ_yy under the centre of contact at depth 0.47127 (node 713)",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Press",
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"nodes": [
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713
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]
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},
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"pointer": "/nodes/0/stress/1"
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},
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"value": -2099.1580228637245,
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"tolerance": {
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"relative": 0.04
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},
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"reason": "σ_z = −p₀ / √(1 + z²/b²) on the axis of a half-plane (Johnson 1985, eq. 4.49); the foundation is ten half-widths wide and deep, not a half-plane, and the stress is the nodal average of the elements around the node"
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}
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]
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} |