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 (2)
| Label | Occurrences |
|---|---|
| Kirchhoff stress tensor canonical | 2 |
| Kirchhoff stress | 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]
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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.
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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.
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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.
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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.
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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
ⓘ
linked to:
Kirchhoff stress tensor
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 ⓘ |
| isSpatialTensor | true ⓘ |
| order | 2 ⓘ |
| property | symmetric for non-polar continua without couple stresses ⓘ |
| relatedTo |
Cauchy stress tensor
ⓘ
deformation gradient ⓘ determinant of deformation gradient ⓘ first Piola–Kirchhoff stress tensor ⓘ
linked to:
Piola–Kirchhoff stress tensors
second Piola–Kirchhoff stress tensor ⓘ |
| relationToCauchyStress | \boldsymbol{\sigma} = J^{-1} \, \boldsymbol{\tau} ⓘ |
| relationToSecondPiolaKirchhoff | \boldsymbol{\tau} = \mathbf{F} \, \mathbf{S} \, \mathbf{F}^T ⓘ |
| 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
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Instruction
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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 (3)
Full triples — surface form annotated when it differs from this entity's canonical label.