Cauchy stress tensor
E239289
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.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Cauchy stress tensor canonical | 2 |
| Cauchy’s stress principle | 1 |
| Mohr’s circle | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2171650 — 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: Cauchy stress tensor Context triple: [Augustin-Louis Cauchy, knownFor, Cauchy stress tensor]
-
A.
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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B.
continuum mechanics
Continuum mechanics is a branch of physics that models the behavior and deformation of materials and fluids by treating them as continuous media rather than discrete particles.
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C.
Einstein tensor
The Einstein tensor is a mathematical object in general relativity that encapsulates how spacetime curvature is related to the distribution of matter and energy.
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D.
Young's modulus
Young's modulus is a fundamental mechanical property that measures the stiffness of a material by quantifying the relationship between stress and strain in the elastic deformation region.
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E.
Navier–Stokes equations
The Navier–Stokes equations are fundamental partial differential equations in fluid mechanics that describe how the velocity field of a fluid evolves under forces like pressure and viscosity.
- 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: Cauchy stress tensor Target entity description: 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.
-
A.
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.
-
B.
continuum mechanics
Continuum mechanics is a branch of physics that models the behavior and deformation of materials and fluids by treating them as continuous media rather than discrete particles.
-
C.
Einstein tensor
The Einstein tensor is a mathematical object in general relativity that encapsulates how spacetime curvature is related to the distribution of matter and energy.
-
D.
Young's modulus
Young's modulus is a fundamental mechanical property that measures the stiffness of a material by quantifying the relationship between stress and strain in the elastic deformation region.
-
E.
Navier–Stokes equations
The Navier–Stokes equations are fundamental partial differential equations in fluid mechanics that describe how the velocity field of a fluid evolves under forces like pressure and viscosity.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
field variable in continuum mechanics
ⓘ
physical quantity ⓘ second-order tensor ⓘ stress measure ⓘ |
| actsOn | oriented surface element ⓘ |
| alsoKnownAs |
true stress
ⓘ
true stress tensor ⓘ |
| assumes | continuum hypothesis ⓘ |
| componentCount | 9 components in 3D ⓘ |
| definedOn |
current configuration of a body
ⓘ
material point ⓘ |
| dependsOn |
spatial position
ⓘ
time ⓘ |
| domain |
deformable solids
ⓘ
fluids ⓘ |
| fieldOfStudy |
continuum mechanics
ⓘ
fluid mechanics ⓘ solid mechanics ⓘ |
| hasComponentType |
normal stress
ⓘ
shear stress ⓘ |
| hasDimension | 3×3 in three-dimensional space ⓘ |
| hasProperty | symmetric in absence of body couples ⓘ |
| hasRank | 2 ⓘ |
| hasUnit |
newton per square metre
ⓘ
pascal ⓘ |
| independentComponentCount | 6 independent components for symmetric case in 3D ⓘ |
| mathematicallyExpressedAs | σ_ij = traction_i on face with normal in j-direction ⓘ |
| namedAfter | Augustin-Louis Cauchy ⓘ |
| relatedTo |
Kirchhoff stress tensor
ⓘ
Cauchy stress tensor self-linksurface differs ⓘ
surface form:
Mohr’s circle
Piola–Kirchhoff stress tensors ⓘ principal stresses ⓘ stress invariants ⓘ |
| relatesTo | traction vector ⓘ |
| represents |
internal distribution of forces in a material
ⓘ
state of stress at a point in a continuum ⓘ |
| satisfies |
Cauchy stress tensor
self-linksurface differs
ⓘ
surface form:
Cauchy’s stress principle
balance of angular momentum ⓘ balance of linear momentum ⓘ |
| usedFor |
constitutive modeling of materials
ⓘ
finite element analysis ⓘ formulating equilibrium equations ⓘ stress analysis in engineering design ⓘ |
| usedIn |
fluid dynamics of viscous flows
ⓘ
linear elasticity ⓘ plasticity theory ⓘ viscoelasticity ⓘ |
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: Cauchy stress tensor Description of subject: 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.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
Augustin-Louis Cauchy
this entity surface form:
Cauchy’s stress principle
this entity surface form:
Mohr’s circle