ReferenceAvailable
Structural Mechanics
Three-dimensional small-strain solid mechanics.
Reference
| Field | Value | Description |
|---|---|---|
| constraints | [] | — |
| coupled_runtime | {"adapter_module":"telion_backend.v2.runtimes.coupled_fields","adjoint_vjp_owner":"StructuralCoupledAdapter","certification":"Generalized-alpha displacement-velocity-acceleration block form using the certified structural mass, damping, gyroscopic, rotating, stiffness, and load operators.","checkpointing":true,"dynamic_state_schema":true,"execution_backend":"telion-v2-shared-execution","gradient_channels":["structural.materials","structural.coordinates","structural.inputs"],"history_depth":2,"history_jacobian_owner":"StructuralCoupledAdapter","jacobian_owner":"StructuralCoupledAdapter","nonlinear_solver":"CoupledNewtonSession","output_vjp_owner":"StructuralCoupledAdapter","requires_spatial_mesh":true,"residual_owner":"StructuralCoupledAdapter","runtime":"telion-coupled-graph","state_fields":["solid.u"],"supported_integrators":["Generalized-alpha"]} | — |
| differentiable_runtime | {"certification":"StructuralDifferentiableRuntime","coordinate_expression_gradient":true,"coordinate_gradient":true,"design_properties":["*"],"execution_backend":"telion-v2-shared-execution","expression_objectives":true,"material_expression_gradient":true,"material_gradient":true,"objective_rules":[{"entity_dimensions":["global"],"modes":["stationary"],"operators":["value"],"supports_selection":false,"symbols":["solid.compliance"],"value_kind":"scalar-global"},{"entity_dimensions":["global","domain","boundary","point"],"modes":["stationary","transient"],"operators":["norm"],"supports_selection":true,"symbols":["solid.u"],"value_kind":"field"},{"entity_dimensions":["global","domain","boundary","point"],"modes":["stationary","transient"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maximum","smooth-minimum"],"supports_selection":true,"symbols":["solid.disp"],"value_kind":"field"},{"entity_dimensions":["global","domain","boundary","point"],"modes":["stationary","transient"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maximum","smooth-minimum"],"supports_selection":true,"symbols":["solid.ux"],"value_kind":"field"},{"entity_dimensions":["global","domain","boundary","point"],"modes":["stationary","transient"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maximum","smooth-minimum"],"supports_selection":true,"symbols":["solid.uy"],"value_kind":"field"},{"entity_dimensions":["global","domain","boundary","point"],"modes":["stationary","transient"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maximum","smooth-minimum"],"supports_selection":true,"symbols":["solid.uz"],"value_kind":"field"},{"entity_dimensions":["global","domain"],"modes":["stationary"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maximum","smooth-minimum"],"supports_selection":true,"symbols":["solid.strain"],"value_kind":"field"},{"entity_dimensions":["global","domain"],"modes":["stationary"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maximum","smooth-minimum"],"supports_selection":true,"symbols":["solid.stress"],"value_kind":"field"},{"entity_dimensions":["global","domain"],"modes":["stationary"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maximum","smooth-minimum"],"supports_selection":true,"symbols":["solid.mises"],"value_kind":"field"},{"entity_dimensions":["global"],"modes":["stationary"],"operators":["value"],"supports_selection":false,"symbols":["solid.strainEnergy"],"value_kind":"scalar-global"},{"entity_dimensions":["global","domain","boundary","point"],"modes":["transient"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maximum","smooth-minimum"],"supports_selection":true,"symbols":["solid.velocity"],"value_kind":"field"},{"entity_dimensions":["global","domain","boundary","point"],"modes":["transient"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maximum","smooth-minimum"],"supports_selection":true,"symbols":["solid.acceleration"],"value_kind":"field"},{"entity_dimensions":["global"],"modes":["transient"],"operators":["norm"],"supports_selection":false,"symbols":["solid.coriolisForce"],"value_kind":"vector-global"},{"entity_dimensions":["global"],"modes":["transient"],"operators":["norm"],"supports_selection":false,"symbols":["solid.rotatingFrameForce"],"value_kind":"vector-global"},{"entity_dimensions":["global"],"modes":["transient"],"operators":["value"],"supports_selection":false,"symbols":["solid.kineticEnergy"],"value_kind":"scalar-global"},{"entity_dimensions":["global"],"modes":["transient"],"operators":["value"],"supports_selection":false,"symbols":["solid.dampingPower"],"value_kind":"scalar-global"}],"residual_owner":"StructuralMechanics.element_residual","state_fields":["u"],"supported_objective_symbols":{"coordinate":["solid.compliance","solid.u","solid.disp","solid.ux","solid.uy","solid.uz","solid.strain","solid.stress","solid.mises","solid.strainEnergy"],"material":["solid.compliance","solid.u","solid.disp","solid.ux","solid.uy","solid.uz","solid.strain","solid.stress","solid.mises","solid.strainEnergy"],"topology":["solid.compliance","solid.u","solid.disp","solid.ux","solid.uy","solid.uz","solid.strain","solid.stress","solid.mises","solid.strainEnergy"]},"topology_expression_gradient":true} | — |
| dynamic_outputs | [] | — |
| equation_summary | div(sigma) + F = rho*(d2u/dt2 + 2*Omega x du/dt + dOmega/dt x r + Omega x (Omega x r) + a_frame) | — |
| frequency_domain_runtime | null | — |
| metadata | {"releaseSupport":{"certifiedStudies":["stationary","transient","eigenfrequency","eigenvalue","parametric-sweep"],"manifest":"docs/september-2026-classroom-physics-matrix.json","manifestSha256":"0a819976ac943e9eedf5bc7f9c80880dd9103cb62bb4c5a915b98c452b135a5c","profile":"september-2026-classroom","reason":"Selectable only for the certified study capabilities declared by Structural Mechanics.","selectable":true}} | — |
| preferred_material | null | — |
| schema_version | 0.1.0 | — |
| stateVariables | [{"adjointDescription":"Structural adjoint solve supports coordinate, material, and expression-objective derivatives for the displacement state.","adjointSupported":true,"availability":{"topologyMethods":[]},"canonicalSymbol":"solid.u","complexValued":false,"componentDescriptions":["X-direction displacement","Y-direction displacement","Z-direction displacement"],"componentNames":["ux","uy","uz"],"componentSymbols":["solid.ux","solid.uy","solid.uz"],"components":3,"description":"Three-dimensional structural displacement field.","differentiability":"exact-ad","displayName":"Displacement","finiteElementSpace":"H1-P1","initialValue":"0","location":"node","name":"u","namingPolicy":"fixed","quantityId":"solid.u","rank":"vector","role":"state","runtimeEvidence":{"certificationFixture":"tests/python_backend/test_differentiable_physics_contract.py::test_builtin_physics_optimization_contract_gate","provider":"StructuralMechanics.element_residual"},"symbolPattern":null,"unit":"m"}] | — |
| studies | [{"certified":true,"differentiability":"exact-ad","kind":"stationary","reason":"september-2026-classroom verified contract: constant-strain and rigid-body patch tests plus global applied-load/reaction balance"},{"certified":true,"differentiability":"exact-ad","kind":"eigenfrequency","reason":"september-2026-classroom verified contract: generalized K phi = lambda M phi residual, positive frequency, and mesh-refinement trend"},{"certified":true,"differentiability":"exact-ad","kind":"eigenvalue","reason":"september-2026-classroom verified contract: physical generalized K phi = lambda M phi residual, lambda units of 1/s^2, mechanical-mass normalization, and inverse-density/direct-stiffness scaling"},{"certified":true,"differentiability":"exact-ad","kind":"parametric-sweep","reason":"september-2026-classroom verified contract: two-point body-load sweep publishes distinct linearly scaled displacement fields on one unchanged mesh"},{"certified":false,"differentiability":"exact-ad","kind":"sensitivity","reason":"Sensitivity is unavailable for this physics interface."},{"certified":false,"differentiability":"exact-ad","kind":"optimization","reason":"Optimization is unavailable for this physics interface."},{"certified":true,"differentiability":"exact-ad","kind":"transient","reason":"september-2026-classroom verified contract: second-order variable-step temporal convergence and monotone spatial eigenfrequency refinement"}] | — |
| transient_runtime | {"capacity_properties":["rho"],"certification":"StructuralDynamicBdfRuntime","checkpointing":true,"design_properties":["E","nu","cE","rho"],"design_property_conditions":{},"design_vjp_owner":"StructuralTransientTopologyRuntime","expression_objectives":true,"gradient_channels":["coordinates","material","input","initial"],"gradient_vjp_owner":"StructuralTransientTopologyRuntime","history_depth":2,"input_gradient":true,"input_vjp_owner":"StructuralTransientTopologyRuntime","observation_vjp_owner":"StructuralTransientTopologyRuntime","residual_linearization_owner":"StructuralTransientTopologyRuntime","runtime":"structural-bdf","state_fields":["u"],"state_reconstruction_owner":"StructuralTransientTopologyRuntime","supported_integrators":["BDF1","BDF2"],"supported_observation_symbols":["solid.u","solid.ux","solid.uy","solid.uz","solid.disp","solid.velocity","solid.acceleration","solid.coriolisForce","solid.rotatingFrameForce","solid.kineticEnergy","solid.dampingPower"],"time_derivative_orders":{"u":2},"topology_gradient":true,"transpose_solve_owner":"StructuralTransientTopologyRuntime"} | — |
| weak_contributions | [{"differentiability":"exact-ad","entity_dimension":"domain","expression":"inner(strain(test(solid.u)), stress(solid.u)) - dot(test(solid.u), solid.F)","name":"solid.balance","test_field":"solid.u"}] | — |
| category | Structural Mechanics | — |
| description | Three-dimensional small-strain solid mechanics. | — |
| dimensions | [3] | — |
| display_name | Structural Mechanics | — |
| kind | Structural Mechanics | — |
| namespace | solid | — |
| status | certified | — |
| visible | true | — |
Three-dimensional small-strain solid mechanics.
Contract
| Property | Value |
|---|---|
| constraints | [] |
| coupled_runtime | {"adapter_module":"telion_backend.v2.runtimes.coupled_fields","adjoint_vjp_owner":"StructuralCoupledAdapter","certification":"Generalized-alpha displacement-velocity-acceleration block form using the certified structural mass, damping, gyroscopic, rotating, stiffness, and load operators.","checkpointing":true,"dynamic_state_schema":true,"execution_backend":"telion-v2-shared-execution","gradient_channels":["structural.materials","structural.coordinates","structural.inputs"],"history_depth":2,"... |
| differentiable_runtime | {"certification":"StructuralDifferentiableRuntime","coordinate_expression_gradient":true,"coordinate_gradient":true,"design_properties":["*"],"execution_backend":"telion-v2-shared-execution","expression_objectives":true,"material_expression_gradient":true,"material_gradient":true,"objective_rules":[{"entity_dimensions":["global"],"modes":["stationary"],"operators":["value"],"supports_selection":false,"symbols":["solid.compliance"],"value_kind":"scalar-global"},{"entity_dimensions":["global","... |
| dynamic_outputs | [] |
| equation_summary | div(sigma) + F = rho*(d2u/dt2 + 2*Omega x du/dt + dOmega/dt x r + Omega x (Omega x r) + a_frame) |
| frequency_domain_runtime | null |
| metadata | {"releaseSupport":{"certifiedStudies":["stationary","transient","eigenfrequency","eigenvalue","parametric-sweep"],"manifest":"docs/september-2026-classroom-physics-matrix.json","manifestSha256":"0a819976ac943e9eedf5bc7f9c80880dd9103cb62bb4c5a915b98c452b135a5c","profile":"september-2026-classroom","reason":"Selectable only for the certified study capabilities declared by Structural Mechanics.","selectable":true}} |
| preferred_material | null |
| schema_version | 0.1.0 |
| stateVariables | [{"adjointDescription":"Structural adjoint solve supports coordinate, material, and expression-objective derivatives for the displacement state.","adjointSupported":true,"availability":{"topologyMethods":[]},"canonicalSymbol":"solid.u","complexValued":false,"componentDescriptions":["X-direction displacement","Y-direction displacement","Z-direction displacement"],"componentNames":["ux","uy","uz"],"componentSymbols":["solid.ux","solid.uy","solid.uz"],"components":3,"description":"Three-dimensio... |
| studies | [{"certified":true,"differentiability":"exact-ad","kind":"stationary","reason":"september-2026-classroom verified contract: constant-strain and rigid-body patch tests plus global applied-load/reaction balance"},{"certified":true,"differentiability":"exact-ad","kind":"eigenfrequency","reason":"september-2026-classroom verified contract: generalized K phi = lambda M phi residual, positive frequency, and mesh-refinement trend"},{"certified":true,"differentiability":"exact-ad","kind":"eigenvalue"... |
| transient_runtime | {"capacity_properties":["rho"],"certification":"StructuralDynamicBdfRuntime","checkpointing":true,"design_properties":["E","nu","cE","rho"],"design_property_conditions":{},"design_vjp_owner":"StructuralTransientTopologyRuntime","expression_objectives":true,"gradient_channels":["coordinates","material","input","initial"],"gradient_vjp_owner":"StructuralTransientTopologyRuntime","history_depth":2,"input_gradient":true,"input_vjp_owner":"StructuralTransientTopologyRuntime","observation_vjp_owner... |
| weak_contributions | [{"differentiability":"exact-ad","entity_dimension":"domain","expression":"inner(strain(test(solid.u)), stress(solid.u)) - dot(test(solid.u), solid.F)","name":"solid.balance","test_field":"solid.u"}] |
| category | Structural Mechanics |
| description | Three-dimensional small-strain solid mechanics. |
| dimensions | [3] |
| display_name | Structural Mechanics |
| kind | Structural Mechanics |
| namespace | solid |
| status | certified |
| visible | true |