Cauchy stress tensor

E239289

field variable in continuum mechanics physical quantity second-order tensor stress measure

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.

Try in SPARQL Jump to: Surface forms Statements Referenced by

All labels observed (3)

Label	Occurrences
Cauchy stress tensor canonical	2
Cauchy’s stress principle	1
Mohr’s circle	1

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.

Augustin-Louis Cauchy → knownFor → Cauchy stress tensor ⓘ

Augustin-Louis → notableFor → Cauchy stress tensor ⓘ

subject surface form: Augustin-Louis Cauchy

Cauchy stress tensor → satisfies → Cauchy stress tensor self-linksurface differs ⓘ

this entity surface form: Cauchy’s stress principle

Cauchy stress tensor → relatedTo → Cauchy stress tensor self-linksurface differs ⓘ

this entity surface form: Mohr’s circle