optimization-physics-contractAvailable
Piezoelectricity
Defines optimization applicability and derivative ownership for Piezoelectricity.
Reference contract
| Field | Value | Description |
|---|---|---|
| kind | Piezoelectricity | — |
| namespace | pze | — |
| status | certified | — |
| visible | true | — |
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| — |
| governingEquations | [{"description":"","differentiability":"exact-ad","editor":null,"entityDimension":"domain","latex":"\\nabla\\!\\cdot\\boldsymbol{\\sigma}+\\mathbf F=\\rho\\,\\ddot{\\mathbf u}","mathml":"<math display=\"block\"><mrow><mo>∇</mo><mo>·</mo><mi mathvariant=\"bold\">σ</mi><mo>+</mo><mi mathvariant=\"bold\">F</mi><mo>=</mo><mi>ρ</mi><mover><mi mathvariant=\"bold\">u</mi><mo>¨</mo></mover></mrow></math>","name":"Mechanical equilibrium","readOnly":true,"section":"governing-equation"},{"description":"","differentiability":"exact-ad","editor":null,"entityDimension":"domain","latex":"\\nabla\\!\\cdot\\mathbf D=\\rho_q","mathml":"<math display=\"block\"><mrow><mo>∇</mo><mo>·</mo><mi mathvariant=\"bold\">D</mi><mo>=</mo><msub><mi>ρ</mi><mi>q</mi></msub></mrow></math>","name":"Gauss law","readOnly":true,"section":"governing-equation"},{"description":"","differentiability":"exact-ad","editor":null,"entityDimension":"domain","latex":"\\boldsymbol{\\sigma}=\\mathsf C^E:\\boldsymbol{\\varepsilon}-\\mathsf e^{\\mathsf T}\\mathbf E","mathml":"<math display=\"block\"><mrow><mi mathvariant=\"bold\">σ</mi><mo>=</mo><msup><mi mathvariant=\"bold\">C</mi><mi>E</mi></msup><mo>:</mo><mi mathvariant=\"bold\">ε</mi><mo>−</mo><msup><mi mathvariant=\"bold\">e</mi><mi>T</mi></msup><mi mathvariant=\"bold\">E</mi></mrow></math>","name":"Piezoelectric stress law","readOnly":true,"section":"definition"},{"description":"","differentiability":"exact-ad","editor":null,"entityDimension":"domain","latex":"\\mathbf D=\\mathsf e:\\boldsymbol{\\varepsilon}+\\boldsymbol{\\epsilon}^{S}\\mathbf E,\\qquad\\mathbf E=-\\nabla V","mathml":"<math display=\"block\"><mrow><mi mathvariant=\"bold\">D</mi><mo>=</mo><mi mathvariant=\"bold\">e</mi><mo>:</mo><mi mathvariant=\"bold\">ε</mi><mo>+</mo><msup><mi mathvariant=\"bold\">ϵ</mi><mi>S</mi></msup><mi mathvariant=\"bold\">E</mi><mo>,</mo><mspace width=\"1em\"/><mi mathvariant=\"bold\">E</mi><mo>=</mo><mo>−</mo><mo>∇</mo><mi>V</mi></mrow></math>","name":"Electric displacement law","readOnly":true,"section":"definition"}] | — |
The runtime provider, evidence fixture, derivative channels, geometric modes, objective symbols, reductions, contribution bindings, and governing equations are generated from the physics catalog.