Kirchhoff stress tensor
E825637
The Kirchhoff stress tensor is a measure of stress in a deforming continuum obtained by scaling the Cauchy stress with the determinant of the deformation gradient, commonly used in finite-strain formulations.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Kirchhoff stress tensor canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T9843817 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Kirchhoff stress tensor Context triple: [Cauchy stress tensor, relatedTo, Kirchhoff stress tensor]
-
A.
Cauchy stress tensor
The Cauchy stress tensor is a fundamental concept in continuum mechanics that mathematically represents the internal distribution of forces (stresses) within a deformable material at a point.
-
B.
Piola–Kirchhoff stress tensors
Piola–Kirchhoff stress tensors are alternative measures of stress in continuum mechanics that describe forces with respect to a material’s reference configuration rather than its current deformed state.
-
C.
Maxwell stress tensor
The Maxwell stress tensor is a mathematical construct in classical electromagnetism that represents how electric and magnetic fields transmit mechanical stresses, such as pressure and tension, through space and matter.
-
D.
Les tenseurs en mécanique et en élasticité
"Les tenseurs en mécanique et en élasticité" is a technical work by Léon Brillouin that presents the mathematical theory and applications of tensors in continuum mechanics and elasticity.
-
E.
stress–energy tensor
The stress–energy tensor is a fundamental object in relativity that encodes the density and flow of energy and momentum in spacetime, acting as the source term for gravitational and electromagnetic field equations.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Kirchhoff stress tensor Target entity description: The Kirchhoff stress tensor is a measure of stress in a deforming continuum obtained by scaling the Cauchy stress with the determinant of the deformation gradient, commonly used in finite-strain formulations.
-
A.
Cauchy stress tensor
The Cauchy stress tensor is a fundamental concept in continuum mechanics that mathematically represents the internal distribution of forces (stresses) within a deformable material at a point.
-
B.
Piola–Kirchhoff stress tensors
Piola–Kirchhoff stress tensors are alternative measures of stress in continuum mechanics that describe forces with respect to a material’s reference configuration rather than its current deformed state.
-
C.
Maxwell stress tensor
The Maxwell stress tensor is a mathematical construct in classical electromagnetism that represents how electric and magnetic fields transmit mechanical stresses, such as pressure and tension, through space and matter.
-
D.
Les tenseurs en mécanique et en élasticité
"Les tenseurs en mécanique et en élasticité" is a technical work by Léon Brillouin that presents the mathematical theory and applications of tensors in continuum mechanics and elasticity.
-
E.
stress–energy tensor
The stress–energy tensor is a fundamental object in relativity that encodes the density and flow of energy and momentum in spacetime, acting as the source term for gravitational and electromagnetic field equations.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
continuum mechanics concept
ⓘ
second-order tensor ⓘ stress measure ⓘ |
| advantage | removes explicit dependence of stress on volume change through J in some formulations ⓘ |
| alsoKnownAs |
Kirchhoff stress
NERFINISHED
ⓘ
weighted Cauchy stress ⓘ |
| appliesTo |
fluids
ⓘ
solids ⓘ viscoelastic materials ⓘ |
| assumes | continuum hypothesis ⓘ |
| category |
spatial stress measure
ⓘ
stress tensor ⓘ |
| definedOn | deforming continuum ⓘ |
| definition | \boldsymbol{\tau} = J \, \boldsymbol{\sigma} ⓘ |
| dependsOn |
Jacobian J = \det \mathbf{F}
ⓘ
current configuration ⓘ deformation gradient F ⓘ |
| dimension | same physical dimension as Cauchy stress ⓘ |
| field |
continuum mechanics
ⓘ
finite-strain theory ⓘ nonlinear solid mechanics ⓘ |
| frame | current (spatial) configuration ⓘ |
| frameIndifference | objective stress measure ⓘ |
| hasComponent | \tau_{ij} ⓘ |
| introducedBy | Gustav Kirchhoff NERFINISHED ⓘ |
| isSpatialTensor | true ⓘ |
| order | 2 ⓘ |
| property | symmetric for non-polar continua without couple stresses ⓘ |
| relatedTo |
Cauchy stress tensor
NERFINISHED
ⓘ
deformation gradient ⓘ determinant of deformation gradient ⓘ first Piola–Kirchhoff stress tensor NERFINISHED ⓘ second Piola–Kirchhoff stress tensor ⓘ |
| relationToCauchyStress | \boldsymbol{\sigma} = J^{-1} \, \boldsymbol{\tau} GENERATED ⓘ |
| relationToSecondPiolaKirchhoff | \boldsymbol{\tau} = \mathbf{F} \, \mathbf{S} \, \mathbf{F}^T GENERATED ⓘ |
| symbol | \boldsymbol{\tau} ⓘ |
| transformation | push-forward of second Piola–Kirchhoff stress ⓘ |
| unit | Pascal ⓘ |
| usedFor |
constitutive modeling at finite strains
ⓘ
formulation of work-conjugate stress–strain pairs ⓘ stress update algorithms in nonlinear FE codes ⓘ |
| usedIn |
computational solid mechanics
ⓘ
finite element method ⓘ finite-strain formulations ⓘ hyperelastic material models ⓘ large-deformation analysis ⓘ |
| workConjugateTo |
logarithmic strain in some formulations
ⓘ
rate of deformation tensor ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Kirchhoff stress tensor Description of subject: The Kirchhoff stress tensor is a measure of stress in a deforming continuum obtained by scaling the Cauchy stress with the determinant of the deformation gradient, commonly used in finite-strain formulations.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.