physics-interfaceAvailable
Piezoelectricity
Coupled linear piezoelectricity.
Reference contract
| Field | Value | Description |
|---|---|---|
| constraints | [] | — |
| coupled_runtime | {"adapter_module":"telion_backend.v2.runtimes.coupled_fields","adjoint_vjp_owner":"PiezoelectricCoupledAdapter","certification":"Structural Mechanics and Electrostatics operators plus the thermodynamically reciprocal piezoelectric cross coupling.","checkpointing":true,"dynamic_state_schema":false,"execution_backend":"telion-v2-shared-execution","gradient_channels":[],"history_depth":2,"history_jacobian_owner":"PiezoelectricCoupledAdapter","jacobian_owner":"PiezoelectricCoupledAdapter","nonlinear_solver":"CoupledNewtonSession","output_vjp_owner":"PiezoelectricCoupledAdapter","requires_spatial_mesh":true,"residual_owner":"PiezoelectricCoupledAdapter","runtime":"telion-coupled-graph","supported_integrators":["BDF1","BDF2"]} | — |
| differentiable_runtime | 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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","boundary","point"],"modes":["stationary"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maximum","smooth-minimum"],"supports_selection":true,"symbols":["pze.mises"],"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","domain"],"modes":["stationary"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maximum","smooth-minimum"],"supports_selection":true,"symbols":["pze.E"],"value_kind":"field"},{"entity_dimensions":["global","domain"],"modes":["stationary"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maximum","smooth-minimum"],"supports_selection":true,"symbols":["pze.D"],"value_kind":"field"},{"entity_dimensions":["global"],"modes":["stationary"],"operators":["value"],"supports_selection":false,"symbols":["pze.energy"],"value_kind":"scalar-global"},{"entity_dimensions":["global"],"modes":["stationary"],"operators":["value"],"supports_selection":false,"symbols":["pze.couplingEnergy"],"value_kind":"scalar-global"},{"entity_dimensions":["global"],"modes":["stationary"],"operators":["value"],"supports_selection":false,"symbols":["solid.strainEnergy"],"value_kind":"scalar-global"},{"entity_dimensions":["global"],"modes":["stationary"],"operators":["value"],"supports_selection":false,"symbols":["es.energy"],"value_kind":"scalar-global"},{"entity_dimensions":["global"],"modes":["stationary"],"operators":["value"],"supports_selection":false,"symbols":["es.compliance"],"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":["pze.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":["pze.acceleration"],"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.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":"Piezoelectricity.element_residual","state_fields":["u","V"],"supported_objective_symbols":{"coordinate":["pze.compliance","solid.compliance","pze.disp","solid.disp","sm.disp","pze.u","solid.u","sm.u","pze.ux","solid.ux","pze.v","solid.uy","pze.w","solid.uz","pze.V","es.V","pze.strain","solid.strain","pze.stress","solid.stress","pze.mises","solid.mises","pze.E","pze.D","pze.energy","pze.couplingEnergy","solid.strainEnergy","es.energy","es.compliance"],"material":["pze.compliance","solid.compliance","pze.disp","solid.disp","sm.disp","pze.u","solid.u","sm.u","pze.ux","solid.ux","pze.v","solid.uy","pze.w","solid.uz","pze.V","es.V","pze.strain","solid.strain","pze.stress","solid.stress","pze.mises","solid.mises","pze.E","pze.D","pze.energy","pze.couplingEnergy","solid.strainEnergy","es.energy","es.compliance"],"topology":["pze.compliance","solid.compliance","pze.disp","solid.disp","sm.disp","pze.u","solid.u","sm.u","pze.ux","solid.ux","pze.v","solid.uy","pze.w","solid.uz","pze.V","es.V"]},"topology_expression_gradient":true} | — |
| dynamic_outputs | [] | — |
| equation_summary | div(sigma)+F=rho*d2u/dt2; div(D)=rho_q; sigma=C:strain-e^T E; D=e:strain+eps E | — |
| frequency_domain_runtime | null | — |
| metadata | {"releaseSupport":{"certifiedStudies":["stationary","eigenfrequency","transient"],"manifest":"docs/september-2026-classroom-physics-matrix.json","manifestSha256":"8f1273eda113099a6658438b1513d127c2c4c99c511c5a6fc5b82637cf6bc949","profile":"september-2026-classroom","reason":"Selectable only for the certified study capabilities declared by this interface.","selectable":true}} | — |
| preferred_material | PZT-5H | — |
| schema_version | 2.0.0 | — |
| studies | [{"certified":true,"differentiability":"exact-ad","kind":"stationary","reason":"september-2026-classroom verified contract: constitutive Jacobian finite-difference agreement and linear displacement scaling with applied voltage"},{"certified":true,"differentiability":"exact-ad","kind":"eigenfrequency","reason":"september-2026-classroom verified contract: coupled mechanical/electrical residuals and monotone spatial refinement"},{"certified":false,"differentiability":"exact-ad","kind":"eigenvalue","reason":"Generic piezoelectric eigenvalues are not certified as physical resonance frequencies; use the certified Eigenfrequency study."},{"certified":false,"differentiability":"exact-ad","kind":"parametric-sweep","reason":"Piezoelectricity parameter-sweep orchestration is not included in the September 2026 classroom support matrix."},{"certified":false,"differentiability":"exact-ad","kind":"sensitivity","reason":"Piezoelectricity sensitivity is disabled until verified per-parameter backend derivative solves are registered."},{"certified":false,"differentiability":"exact-ad","kind":"optimization","reason":"Piezoelectricity optimization is outside the September 2026 classroom support matrix."},{"certified":true,"differentiability":"exact-ad","kind":"transient","reason":"september-2026-classroom verified contract: second-order coupled modal time convergence with distinct variable-step operators"}] | — |
| transient_runtime | {"capacity_properties":["rho"],"certification":"PiezoelectricDynamicBdfRuntime","checkpointing":true,"design_properties":["cE","e","epsS","rho"],"design_property_conditions":{"rho":["Damping","Rotating Frame"]},"design_vjp_owner":"PiezoelectricTransientTopologyRuntime","expression_objectives":true,"gradient_channels":["coordinates","material","input","initial"],"gradient_vjp_owner":"PiezoelectricTransientTopologyRuntime","history_depth":2,"input_gradient":true,"input_vjp_owner":"PiezoelectricTransientTopologyRuntime","observation_vjp_owner":"PiezoelectricTransientTopologyRuntime","residual_linearization_owner":"PiezoelectricTransientTopologyRuntime","runtime":"piezoelectric-bdf","state_fields":["u","V"],"state_reconstruction_owner":"PiezoelectricTransientTopologyRuntime","supported_integrators":["BDF1","BDF2"],"supported_observation_symbols":["pze.u","pze.ux","pze.v","pze.w","pze.disp","pze.V","es.V","solid.u","pze.velocity","pze.acceleration","solid.velocity","solid.acceleration","solid.coriolisForce","solid.rotatingFrameForce","solid.kineticEnergy","solid.dampingPower"],"time_derivative_orders":{"V":0,"u":2},"topology_gradient":true,"transpose_solve_owner":"PiezoelectricTransientTopologyRuntime"} | — |
| weak_contributions | [] | — |
| category | Structural Mechanics / AC/DC | — |
| description | Coupled linear piezoelectricity. | — |
| dimensions | [3] | — |
| display_name | Piezoelectricity | — |
| kind | Piezoelectricity | — |
| namespace | pze | — |
| status | certified | — |
| visible | true | — |
Coupled linear piezoelectricity.
Contract
| Property | Value |
|---|---|
| constraints | [] |
| coupled_runtime | {"adapter_module":"telion_backend.v2.runtimes.coupled_fields","adjoint_vjp_owner":"PiezoelectricCoupledAdapter","certification":"Structural Mechanics and Electrostatics operators plus the thermodynamically reciprocal piezoelectric cross coupling.","checkpointing":true,"dynamic_state_schema":false,"execution_backend":"telion-v2-shared-execution","gradient_channels":[],"history_depth":2,"history_jacobian_owner":"PiezoelectricCoupledAdapter","jacobian_owner":"PiezoelectricCoupledAdapter","nonlin... |
| differentiable_runtime | {"certification":"PiezoelectricDifferentiableRuntime","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":["pze.compliance"],"value_kind":"scalar-global"},{"entity_dimensions":["global"]... |
| dynamic_outputs | [] |
| equation_summary | div(sigma)+F=rho*d2u/dt2; div(D)=rho_q; sigma=C:strain-e^T E; D=e:strain+eps E |
| frequency_domain_runtime | null |
| metadata | {"releaseSupport":{"certifiedStudies":["stationary","eigenfrequency","transient"],"manifest":"docs/september-2026-classroom-physics-matrix.json","manifestSha256":"8f1273eda113099a6658438b1513d127c2c4c99c511c5a6fc5b82637cf6bc949","profile":"september-2026-classroom","reason":"Selectable only for the certified study capabilities declared by this interface.","selectable":true}} |
| preferred_material | PZT-5H |
| schema_version | 2.0.0 |
| studies | [{"certified":true,"differentiability":"exact-ad","kind":"stationary","reason":"september-2026-classroom verified contract: constitutive Jacobian finite-difference agreement and linear displacement scaling with applied voltage"},{"certified":true,"differentiability":"exact-ad","kind":"eigenfrequency","reason":"september-2026-classroom verified contract: coupled mechanical/electrical residuals and monotone spatial refinement"},{"certified":false,"differentiability":"exact-ad","kind":"eigenvalu... |
| transient_runtime | {"capacity_properties":["rho"],"certification":"PiezoelectricDynamicBdfRuntime","checkpointing":true,"design_properties":["cE","e","epsS","rho"],"design_property_conditions":{"rho":["Damping","Rotating Frame"]},"design_vjp_owner":"PiezoelectricTransientTopologyRuntime","expression_objectives":true,"gradient_channels":["coordinates","material","input","initial"],"gradient_vjp_owner":"PiezoelectricTransientTopologyRuntime","history_depth":2,"input_gradient":true,"input_vjp_owner":"Piezoelectric... |
| weak_contributions | [] |
| category | Structural Mechanics / AC/DC |
| description | Coupled linear piezoelectricity. |
| dimensions | [3] |
| display_name | Piezoelectricity |
| kind | Piezoelectricity |
| namespace | pze |
| status | certified |
| visible | true |