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.
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 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.