physics-interfaceAvailable
Structural Mechanics
Three-dimensional small-strain solid mechanics.
Reference contract
| 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","residual_owner":"StructuralCoupledAdapter","runtime":"telion-coupled-graph","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,"residual_owner":"StructuralMechanics.element_residual","state_fields":["u"],"supported_objective_symbols":{"coordinate":["solid.compliance","sm.compliance","solid.u","solid.disp"],"material":["solid.compliance","sm.compliance","solid.u","solid.disp"],"topology":["solid.compliance","sm.compliance","solid.u","solid.disp"]},"topology_expression_gradient":true} | — |
| 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"],"manifest":"docs/september-2026-classroom-physics-matrix.json","manifestSha256":"fe4b2f9ddfee4fe815ba0df4bb22b364a70e095773b56cf79e6d360935757003","profile":"september-2026-classroom","reason":"Selectable only for the certified study capabilities declared by Structural Mechanics.","selectable":true}} | — |
| preferred_material | null | — |
| schema_version | 2.0.0 | — |
| 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":false,"differentiability":"exact-ad","kind":"parametric-sweep","reason":"Structural Mechanics parameter-sweep orchestration is not included in the September 2026 classroom support matrix."},{"certified":false,"differentiability":"exact-ad","kind":"sensitivity","reason":"Structural Mechanics sensitivity is disabled until verified per-parameter backend derivative solves are registered."},{"certified":false,"differentiability":"exact-ad","kind":"optimization","reason":"Structural Mechanics optimization is outside the September 2026 classroom support matrix."},{"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","cE","rho"],"design_vjp_owner":"StructuralTransientTopologyRuntime","expression_objectives":true,"gradient_channels":["coordinates"],"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.v","solid.w","solid.disp","sm.u","sm.disp"],"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,"residual_owner":"StructuralMechanics.element_residual","state_fields":["u"],"supported_objective_symbols":{"coordinate":["solid.compliance","sm.compliance","solid.u","solid.disp"],"material":["solid.compliance","sm.... |
| 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"],"manifest":"docs/september-2026-classroom-physics-matrix.json","manifestSha256":"fe4b2f9ddfee4fe815ba0df4bb22b364a70e095773b56cf79e6d360935757003","profile":"september-2026-classroom","reason":"Selectable only for the certified study capabilities declared by Structural Mechanics.","selectable":true}} |
| preferred_material | null |
| schema_version | 2.0.0 |
| 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","cE","rho"],"design_vjp_owner":"StructuralTransientTopologyRuntime","expression_objectives":true,"gradient_channels":["coordinates"],"gradient_vjp_owner":"StructuralTransientTopologyRuntime","history_depth":2,"input_gradient":true,"input_vjp_owner":"StructuralTransientTopologyRuntime","observation_vjp_owner":"StructuralTransientTopologyRuntime","residual_linearization_own... |
| 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 |