Dental restoration / Illustrative model
See all model results and checks
Support location and crown contact change the model response
Every length, stiffness and load is illustrative. The rigid crown does not model restored enamel thickness, biological healing, human mobility thresholds or stable position after support withdrawal.
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],
"spatial_nonidentifiability": {
"alias": {
"id": "spatial_alias",
"kind": "spatial_alias",
"multiplier": 1.0,
"alias_amplitude": 0.8
},
"reference_matrix": [
[
2.075,
0.0,
1.075
],
[
0.0,
0.8,
1.734723475976807e-18
],
[
1.075,
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0.7551666666666669
]
],
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[
2.075,
0.0,
1.075
],
[
0.0,
0.8,
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],
[
1.075,
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]
],
"matrix_max_absolute_difference": 0.0,
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],
"alternative_delta_q": [
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1.1136016965654399e-17,
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],
"density_min": 0.19999999999999996,
"density_max": 1.8,
"reason": "P3(2y+1) is orthogonal on [-1,0] to polynomials of degree <=2. Rigid-body spring assembly contains only zeroth, first and second moments of side density. Three-point Gauss integrates degree <=5 exactly.",
"local_reaction_ratio_at_right_cervical_endpoint": 1.8,
"local_reaction_ratio_at_right_apical_endpoint": 0.19999999999999996,
"claim": "Exact continuum alias within this reduced model, not an assertion that real PDL follows this density law"
},
"resting_pose_example": {
"reference": {
"support_id": "reference",
"contact_id": "reference_lever",
"matrix": [
[
2.075,
0.0,
1.075
],
[
0.0,
0.8,
1.734723475976807e-18
],
[
1.075,
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],
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1.0,
0.0,
-0.5
],
"delta_q": [
3.1425301094982876,
1.1136016965654399e-17,
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],
"resting_q": [
0.0,
0.0,
0.0
],
"total_q": [
3.1425301094982876,
1.1136016965654399e-17,
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],
"contact_delta": [
5.7103207965722165,
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],
"contact_compliance": 5.7103207965722165,
"integrated_reaction": [
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2.7755575615628914e-17,
0.4999999999999984
],
"force_moment_residual": [
3.3306690738754696e-16,
2.7755575615628914e-17,
-1.609823385706477e-15
],
"foundation_energy": 2.8551603982861034,
"half_load_work": 2.8551603982861082,
"supported_boundary_length": 2.3
},
"wrong_resting_pose": {
"support_id": "reference",
"contact_id": "reference_lever",
"matrix": [
[
2.075,
0.0,
1.075
],
[
0.0,
0.8,
1.734723475976807e-18
],
[
1.075,
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0.7551666666666669
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],
"generalized_load": [
1.0,
0.0,
-0.5
],
"delta_q": [
3.1425301094982876,
1.1136016965654399e-17,
-5.135581374147858
],
"resting_q": [
0.02,
0.0,
0.01
],
"total_q": [
3.1625301094982876,
1.1136016965654399e-17,
-5.125581374147858
],
"contact_delta": [
5.7103207965722165,
1.1136016965654399e-17
],
"contact_compliance": 5.7103207965722165,
"integrated_reaction": [
-0.9999999999999997,
2.7755575615628914e-17,
0.4999999999999984
],
"force_moment_residual": [
3.3306690738754696e-16,
2.7755575615628914e-17,
-1.609823385706477e-15
],
"foundation_energy": 2.8551603982861034,
"half_load_work": 2.8551603982861082,
"supported_boundary_length": 2.3
},
"zero_load_pose_after_reversible_unloading": [
0.02,
0.0,
0.01
],
"claim": "Same incremental mobility can coexist with an imposed wrong resting pose. Unloading recovers that imposed pose; trauma, healing and drift were not simulated."
},
"max_force_moment_residual": 2.1094237467877974e-15,
"max_energy_identity_absolute_error": 3.552713678800501e-14,
"limits": [
"Unit forces define linear response coefficients, not finite physical deformations or recommended human loads.",
"Rigid crown/root omits enamel, dentin and pulp deformation, restored thickness, crack propagation, contact area and fatigue.",
"Small-displacement static elasticity cannot predict healing, permanent repositioning, drift after support withdrawal, perfusion or physiological acceptance thresholds.",
"Very stiff illustrative support is not a diagnostic signature or a biological simulation of ankylosis."
]
}