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OneCAD-Simulation/tests/oracle/nl-contact-patch-axisymmetric/expected.json
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jyvikoandClaude Opus 5.5 227c4544ed solver: mortar contact in 2D models 
Plane strain, plane stress and axisymmetric models take contact pairs and
general (self) contact on the linear edges of tri3 and quad4 elements:
edges oriented out of their elements, the edge mortar of fem with the
thickness or 2 pi r in the weights, the element's area over the edge's
length as the thickness under it, and the in-plane rows of the tangent
blocks. Verified by the contact patch test in plane strain and
axisymmetric (to 1e-9 small sliding, 1e-4 finite), Hertz's line contact
on quad4 edges (Johnson 1985, 4.3; equal to the hex8 model's to 1e-5),
and a hybrid rubber C-ring closing on itself that moves node for node as
the one-layer solid ring.

Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
2026-10-14 16:30:44 -04:00

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{
"title": "Contact patch test, axisymmetric: two rings with non-matching edges in axial compression (implicit mortar contact)",
"kind": "theory",
"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; passed by 2D mortar methods: Yang, Laursen & Meng, IJNME 62:1183–1225, 2005. Uniaxial stress between frictionless supports is uniform in both blocks",
"quantities": [
{
"id": "small_lower_corner",
"quantity": "Small: σ_yy of element 4 over that of element 7",
"measure": {
"command": "solve.probe",
"params": {
"step": "Small",
"elements": [
4
]
},
"pointer": "/elements/0/stress/0/1",
"over": {
"command": "solve.probe",
"params": {
"step": "Small",
"elements": [
7
]
},
"pointer": "/elements/0/stress/0/1"
}
},
"value": 1.0,
"tolerance": {
"relative": 1e-06
},
"reason": "small sliding is linear and its edge mortar integrals exact (degree-3 Gauss on the overlaps): the uniform stress is the discrete solution up to the convergence tolerance"
},
{
"id": "small_lower_far",
"quantity": "Small: σ_yy of element 6 over that of element 7",
"measure": {
"command": "solve.probe",
"params": {
"step": "Small",
"elements": [
6
]
},
"pointer": "/elements/0/stress/0/1",
"over": {
"command": "solve.probe",
"params": {
"step": "Small",
"elements": [
7
]
},
"pointer": "/elements/0/stress/0/1"
}
},
"value": 1.0,
"tolerance": {
"relative": 1e-06
},
"reason": "as for the corner element"
},
{
"id": "small_lower_base",
"quantity": "Small: σ_yy of element 1 over that of element 7",
"measure": {
"command": "solve.probe",
"params": {
"step": "Small",
"elements": [
1
]
},
"pointer": "/elements/0/stress/0/1",
"over": {
"command": "solve.probe",
"params": {
"step": "Small",
"elements": [
7
]
},
"pointer": "/elements/0/stress/0/1"
}
},
"value": 1.0,
"tolerance": {
"relative": 1e-06
},
"reason": "as for the corner element"
},
{
"id": "small_upper_top",
"quantity": "Small: σ_yy of element 10 over that of element 7",
"measure": {
"command": "solve.probe",
"params": {
"step": "Small",
"elements": [
10
]
},
"pointer": "/elements/0/stress/0/1",
"over": {
"command": "solve.probe",
"params": {
"step": "Small",
"elements": [
7
]
},
"pointer": "/elements/0/stress/0/1"
}
},
"value": 1.0,
"tolerance": {
"relative": 1e-06
},
"reason": "as for the corner element"
},
{
"id": "small_lateral",
"quantity": "Small: σ_xx of element 6 over its σ_yy (uniaxial stress: 0)",
"measure": {
"command": "solve.probe",
"params": {
"step": "Small",
"elements": [
6
]
},
"pointer": "/elements/0/stress/0/0",
"over": {
"command": "solve.probe",
"params": {
"step": "Small",
"elements": [
6
]
},
"pointer": "/elements/0/stress/0/1"
}
},
"value": 0.0,
"tolerance": {
"absolute": 1e-06
},
"reason": "a frictionless interface (and symmetry plane) leaves the blocks free to expand sideways; the non-matching interface must not hold them"
},
{
"id": "small_pressure",
"quantity": "Small: the contact pressure at the secondary node (1.5, 1) over −σ_yy of element 7",
"measure": {
"command": "solve.probe",
"params": {
"step": "Small",
"at": [
[
1.5,
1.0,
0.0
]
]
},
"pointer": "/nodes/0/contact/0/pressure",
"over": {
"command": "solve.probe",
"params": {
"step": "Small",
"elements": [
7
]
},
"pointer": "/elements/0/stress/0/1",
"scale": -1.0
}
},
"value": 1.0,
"tolerance": {
"relative": 1e-06
},
"reason": "the mortar multipliers are the nodal values of the contact pressure, uniform and equal to the stress across the interface"
},
{
"id": "small_force",
"quantity": "Small: the integrated contact pressure over the reaction at the pushed top",
"measure": {
"from": "small",
"pointer": "/contacts/0/normal_force",
"over": {
"command": "results.reactions",
"params": {
"step": "Small",
"sets": [
"top"
]
},
"pointer": "/sets/0/force/1",
"scale": -1.0
}
},
"value": 1.0,
"tolerance": {
"relative": 1e-06
},
"reason": "the pressure carries the whole load across the interface (both are totals over the circumference)"
},
{
"id": "finite_lower_corner",
"quantity": "Finite: σ_yy of element 4 over that of element 7",
"measure": {
"command": "solve.probe",
"params": {
"step": "Finite",
"elements": [
4
]
},
"pointer": "/elements/0/stress/0/1",
"over": {
"command": "solve.probe",
"params": {
"step": "Finite",
"elements": [
7
]
},
"pointer": "/elements/0/stress/0/1"
}
},
"value": 1.0,
"tolerance": {
"relative": 0.0002
},
"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"
},
{
"id": "finite_lower_far",
"quantity": "Finite: σ_yy of element 6 over that of element 7",
"measure": {
"command": "solve.probe",
"params": {
"step": "Finite",
"elements": [
6
]
},
"pointer": "/elements/0/stress/0/1",
"over": {
"command": "solve.probe",
"params": {
"step": "Finite",
"elements": [
7
]
},
"pointer": "/elements/0/stress/0/1"
}
},
"value": 1.0,
"tolerance": {
"relative": 0.0002
},
"reason": "as for the corner element"
},
{
"id": "finite_lower_base",
"quantity": "Finite: σ_yy of element 1 over that of element 7",
"measure": {
"command": "solve.probe",
"params": {
"step": "Finite",
"elements": [
1
]
},
"pointer": "/elements/0/stress/0/1",
"over": {
"command": "solve.probe",
"params": {
"step": "Finite",
"elements": [
7
]
},
"pointer": "/elements/0/stress/0/1"
}
},
"value": 1.0,
"tolerance": {
"relative": 0.0002
},
"reason": "as for the corner element"
},
{
"id": "finite_upper_top",
"quantity": "Finite: σ_yy of element 10 over that of element 7",
"measure": {
"command": "solve.probe",
"params": {
"step": "Finite",
"elements": [
10
]
},
"pointer": "/elements/0/stress/0/1",
"over": {
"command": "solve.probe",
"params": {
"step": "Finite",
"elements": [
7
]
},
"pointer": "/elements/0/stress/0/1"
}
},
"value": 1.0,
"tolerance": {
"relative": 0.0002
},
"reason": "as for the corner element"
},
{
"id": "finite_lateral",
"quantity": "Finite: σ_xx of element 6 over its σ_yy (uniaxial stress: 0)",
"measure": {
"command": "solve.probe",
"params": {
"step": "Finite",
"elements": [
6
]
},
"pointer": "/elements/0/stress/0/0",
"over": {
"command": "solve.probe",
"params": {
"step": "Finite",
"elements": [
6
]
},
"pointer": "/elements/0/stress/0/1"
}
},
"value": 0.0,
"tolerance": {
"absolute": 0.0002
},
"reason": "a frictionless interface (and symmetry plane) leaves the blocks free to expand sideways; the non-matching interface must not hold them"
},
{
"id": "finite_pressure",
"quantity": "Finite: the contact pressure at the secondary node (1.5, 1) over −σ_yy of element 7",
"measure": {
"command": "solve.probe",
"params": {
"step": "Finite",
"at": [
[
1.5,
1.0,
0.0
]
]
},
"pointer": "/nodes/0/contact/0/pressure",
"over": {
"command": "solve.probe",
"params": {
"step": "Finite",
"elements": [
7
]
},
"pointer": "/elements/0/stress/0/1",
"scale": -1.0
}
},
"value": 1.0,
"tolerance": {
"relative": 0.0002
},
"reason": "the mortar multipliers are the nodal values of the contact pressure, uniform and equal to the stress across the interface"
},
{
"id": "finite_force",
"quantity": "Finite: the integrated contact pressure over the reaction at the pushed top",
"measure": {
"from": "finite",
"pointer": "/contacts/0/normal_force",
"over": {
"command": "results.reactions",
"params": {
"step": "Finite",
"sets": [
"top"
]
},
"pointer": "/sets/0/force/1",
"scale": -1.0
}
},
"value": 1.0,
"tolerance": {
"relative": 0.0002
},
"reason": "the pressure carries the whole load across the interface (both are totals over the circumference)"
},
{
"id": "small_stress",
"quantity": "Small: σ_yy of element 7 (uniaxial stress E ε = −10 for the 1% squeeze)",
"measure": {
"command": "solve.probe",
"params": {
"step": "Small",
"elements": [
7
]
},
"pointer": "/elements/0/stress/0/1"
},
"value": -10.0,
"tolerance": {
"relative": 0.0001
},
"reason": "the squeeze less the penetration the augmented Lagrangian leaves (up to 10⁻⁵ of the element thickness)"
}
]
}
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