forked from 1b-agent/fieldcraft-upstream
verification: implicit contact patch test and Hertz line contact
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 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
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jyvikoandClaude Opus 5.5 authored and Irakli Kourtis committed
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{
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"title": "Contact patch test: two blocks with non-matching meshes in uniaxial compression (implicit mortar contact)",
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"kind": "theory",
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"source": "The contact patch test: a contact discretisation must transmit a uniform pressure across a non-matching interface exactly; Taylor & Papadopoulos, On a patch test for contact problems in two dimensions, Nonlinear Computational Mechanics, Springer 1991, 690–702; Crisfield, Re-visiting the contact patch test, IJNME 48:435–449, 2000; passed by mortar methods: Puso & Laursen, CMAME 193:601–629, 2004. Uniaxial stress between frictionless symmetry planes is uniform in both blocks",
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"quantities": [
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{
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"id": "small_lower_corner",
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"quantity": "Small: σ_zz of the lower block's corner element under the interface (element 10) over that of the upper block's corner element over it (element 19)",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Small",
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"elements": [
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10
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]
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},
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"pointer": "/elements/0/stress/0/2",
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"over": {
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"command": "solve.probe",
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"params": {
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"step": "Small",
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"elements": [
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19
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]
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},
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"pointer": "/elements/0/stress/0/2"
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}
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},
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"value": 1.0,
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"tolerance": {
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"relative": 1e-06
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},
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"reason": "small sliding is linear and its mortar integrals exact on these rectangular faces: a uniform stress is the discrete solution up to the convergence tolerance (10⁻¹⁰)"
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},
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{
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"id": "small_lower_centre",
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"quantity": "Small: σ_zz of the lower block's centre element under the interface (element 14) over that of element 19",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Small",
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"elements": [
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14
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]
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},
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"pointer": "/elements/0/stress/0/2",
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"over": {
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"command": "solve.probe",
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"params": {
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"step": "Small",
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"elements": [
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19
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]
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},
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"pointer": "/elements/0/stress/0/2"
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}
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},
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"value": 1.0,
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"tolerance": {
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"relative": 1e-06
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},
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"reason": "as for the corner element"
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},
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{
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"id": "small_lower_base",
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"quantity": "Small: σ_zz of the lower block's bottom corner element (element 1) over that of element 19",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Small",
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"elements": [
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1
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]
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},
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"pointer": "/elements/0/stress/0/2",
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"over": {
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"command": "solve.probe",
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"params": {
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"step": "Small",
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"elements": [
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19
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]
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},
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"pointer": "/elements/0/stress/0/2"
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}
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},
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"value": 1.0,
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"tolerance": {
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"relative": 1e-06
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},
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"reason": "as for the corner element"
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},
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{
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"id": "small_upper_top",
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"quantity": "Small: σ_zz of the upper block's top far corner element (element 26) over that of element 19",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Small",
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"elements": [
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26
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]
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},
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"pointer": "/elements/0/stress/0/2",
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"over": {
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"command": "solve.probe",
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"params": {
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"step": "Small",
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"elements": [
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19
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]
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},
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"pointer": "/elements/0/stress/0/2"
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}
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},
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"value": 1.0,
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"tolerance": {
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"relative": 1e-06
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},
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"reason": "as for the corner element"
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},
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{
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"id": "small_lateral",
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"quantity": "Small: σ_xx of element 14 over its σ_zz (uniaxial stress: 0)",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Small",
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"elements": [
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14
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]
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},
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"pointer": "/elements/0/stress/0/0",
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"over": {
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"command": "solve.probe",
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"params": {
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"step": "Small",
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"elements": [
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14
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]
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},
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"pointer": "/elements/0/stress/0/2"
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}
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},
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"value": 0.0,
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"tolerance": {
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"absolute": 1e-06
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},
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"reason": "frictionless symmetry planes and a frictionless interface leave the blocks free to expand sideways; the non-matching interface must not hold them"
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},
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{
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"id": "small_pressure",
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"quantity": "Small: the contact pressure at the secondary node (0.5, 0.5, 1) over −σ_zz of element 19",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Small",
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"at": [
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[
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0.5,
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0.5,
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1.0
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]
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]
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},
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"pointer": "/nodes/0/contact/0/pressure",
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"over": {
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"command": "solve.probe",
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"params": {
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"step": "Small",
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"elements": [
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19
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]
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},
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"pointer": "/elements/0/stress/0/2",
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"scale": -1.0
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}
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},
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"value": 1.0,
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"tolerance": {
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"relative": 1e-06
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},
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"reason": "the mortar multipliers are the nodal values of the contact pressure, uniform and equal to the stress across the interface"
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},
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{
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"id": "small_force",
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"quantity": "Small: the integrated contact pressure over the reaction at the pushed top",
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"measure": {
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"from": "small",
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"pointer": "/contacts/0/normal_force",
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"over": {
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"command": "results.reactions",
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"params": {
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"step": "Small",
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"sets": [
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"top"
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]
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},
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"pointer": "/sets/0/force/2",
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"scale": -1.0
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}
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},
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"value": 1.0,
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"tolerance": {
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"relative": 1e-06
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},
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"reason": "the pressure carries the whole load across the interface"
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},
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{
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"id": "finite_lower_corner",
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"quantity": "Finite: σ_zz of the lower block's corner element under the interface (element 10) over that of the upper block's corner element over it (element 19)",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Finite",
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"elements": [
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10
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]
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},
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"pointer": "/elements/0/stress/0/2",
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"over": {
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"command": "solve.probe",
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"params": {
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"step": "Finite",
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"elements": [
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19
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]
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},
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"pointer": "/elements/0/stress/0/2"
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}
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},
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"value": 1.0,
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"tolerance": {
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"relative": 0.0002
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},
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"reason": "finite sliding is exact up to the geometric terms of the gaps the augmentation leaves (10⁻⁵ of the element thickness) and the default convergence tolerances"
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},
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{
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"id": "finite_lower_centre",
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"quantity": "Finite: σ_zz of the lower block's centre element under the interface (element 14) over that of element 19",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Finite",
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"elements": [
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14
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]
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},
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"pointer": "/elements/0/stress/0/2",
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"over": {
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"command": "solve.probe",
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"params": {
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"step": "Finite",
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"elements": [
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19
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]
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},
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"pointer": "/elements/0/stress/0/2"
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}
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},
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"value": 1.0,
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"tolerance": {
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"relative": 0.0002
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},
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"reason": "as for the corner element"
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},
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{
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"id": "finite_lower_base",
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"quantity": "Finite: σ_zz of the lower block's bottom corner element (element 1) over that of element 19",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Finite",
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"elements": [
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1
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]
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},
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"pointer": "/elements/0/stress/0/2",
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"over": {
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"command": "solve.probe",
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"params": {
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"step": "Finite",
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"elements": [
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19
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]
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},
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"pointer": "/elements/0/stress/0/2"
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}
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},
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"value": 1.0,
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"tolerance": {
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"relative": 0.0002
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},
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"reason": "as for the corner element"
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},
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{
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"id": "finite_upper_top",
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"quantity": "Finite: σ_zz of the upper block's top far corner element (element 26) over that of element 19",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Finite",
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"elements": [
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26
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]
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},
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"pointer": "/elements/0/stress/0/2",
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"over": {
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"command": "solve.probe",
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"params": {
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"step": "Finite",
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"elements": [
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19
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]
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},
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"pointer": "/elements/0/stress/0/2"
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}
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},
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"value": 1.0,
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"tolerance": {
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"relative": 0.0002
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},
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"reason": "as for the corner element"
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},
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{
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"id": "finite_lateral",
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"quantity": "Finite: σ_xx of element 14 over its σ_zz (uniaxial stress: 0)",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Finite",
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"elements": [
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14
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]
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},
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"pointer": "/elements/0/stress/0/0",
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"over": {
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"command": "solve.probe",
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"params": {
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"step": "Finite",
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"elements": [
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14
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]
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},
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"pointer": "/elements/0/stress/0/2"
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}
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},
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"value": 0.0,
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"tolerance": {
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"absolute": 0.0002
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},
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"reason": "frictionless symmetry planes and a frictionless interface leave the blocks free to expand sideways; the non-matching interface must not hold them"
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},
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{
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"id": "finite_pressure",
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"quantity": "Finite: the contact pressure at the secondary node (0.5, 0.5, 1) over −σ_zz of element 19",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Finite",
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"at": [
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[
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0.5,
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0.5,
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1.0
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]
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]
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},
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"pointer": "/nodes/0/contact/0/pressure",
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"over": {
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"command": "solve.probe",
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"params": {
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"step": "Finite",
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"elements": [
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19
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]
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},
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"pointer": "/elements/0/stress/0/2",
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"scale": -1.0
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}
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},
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"value": 1.0,
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"tolerance": {
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"relative": 0.0002
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},
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"reason": "the mortar multipliers are the nodal values of the contact pressure, uniform and equal to the stress across the interface"
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},
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{
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"id": "finite_force",
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"quantity": "Finite: the integrated contact pressure over the reaction at the pushed top",
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"measure": {
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"from": "finite",
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"pointer": "/contacts/0/normal_force",
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"over": {
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"command": "results.reactions",
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"params": {
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"step": "Finite",
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"sets": [
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"top"
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]
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},
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"pointer": "/sets/0/force/2",
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"scale": -1.0
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}
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},
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"value": 1.0,
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"tolerance": {
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"relative": 0.0002
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},
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"reason": "the pressure carries the whole load across the interface"
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},
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{
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"id": "small_stress",
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"quantity": "Small: σ_zz of element 19 (uniaxial stress E ε = −10 for the 1% squeeze)",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Small",
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"elements": [
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19
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]
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},
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"pointer": "/elements/0/stress/0/2"
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},
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"value": -10.0,
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"tolerance": {
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"relative": 0.0001
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},
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"reason": "the squeeze less the penetration the augmented Lagrangian leaves (up to 10⁻⁵ of the element thickness, a few 10⁻⁵ of the squeeze)"
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}
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]
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}
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Reference in new issue
Block a user