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Cauchy stress tensor

In continuum mechanics, the Cauchy stress tensor (symbol ⁠ σ {\displaystyle {\boldsymbol {\sigma }}} ⁠, named after Augustin-Louis Cauchy), also called true stress tensor or simply stress tensor, completely defines the state of stress at a point inside a material in the deformed state, placement, or configuration. The second order tensor consists of nine…

Measurement, Cauchy's stress theorem—stress tensor & Euler–Cauchy stress principle – stress vector

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Cauchy's stress theorem—stress tensor

Tensor fieldTetrahedronInfinitesimalEuler's first law of motionUnit vector
17 related topics

Euler–Cauchy stress principle – stress vector

NewtonEulerForcesSurface forcesBody forces
13 related topics

Principal stresses and stress invariants

Physical quantityInvariantsMagnitudeCartesian coordinate systemNormal
12 related topics

Overview

Continuum mechanicsAugustin-Louis CauchyStress tensor is symmetricDeformedTensor
28 related topics

Key facts & relationships

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Behaviour under coord transformation
tensor
Common symbols
σ
Dimension
L − 1 M T − 2 {\displaystyle {\mathsf {L}}^{-1}{\mathsf {M}}{\mathsf {T}}^{-2}}
In SI base units
Pa = kg⋅m−1⋅s−2
Other units
Pound per square inch (psi), bar
SI unit
pascal (Pa)

Topics to explore

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Overview

Euler–Cauchy stress principle – stress vector

Cauchy's stress theorem—stress tensor

Balance laws – Cauchy's equations of motion

Principal stresses and stress invariants

Stress deviator tensor

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Cauchy stress tensor

Nodes87
Edges86
Triples12
Avg. degree1.98
Density0.022989
Components1

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Cauchy stress tensor

Top relations

related to Cauchy's stress theorem—stress tensor · 4
Cauchy stress tensor → Cauchy, Cauchy's, However, The
related to Cauchy's first law of motion · 2
Cauchy stress tensor → According, Cauchy
Behaviour under coord transformation · 1
Cauchy stress tensor → tensor
Common symbols · 1
Cauchy stress tensor → σ
Dimension · 1
Cauchy stress tensor → L − 1 M T − 2 {\displaystyle {\mathsf {L}}^{-1}{\mathsf {M}}{\mathsf {T}}^{-2}}
In SI base units · 1
Cauchy stress tensor → Pa = kg⋅m−1⋅s−2
Other units · 1
Cauchy stress tensor → Pound per square inch (psi), bar
SI unit · 1
Cauchy stress tensor → pascal (Pa)

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Important terminology

stress tensor displaystyle vector normal point plane principal cauchy components coordinate called stresses system unit sigma also mathbf body shear

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Cauchy stress tensorBehaviour under coord transformationtensor1.00infobox
Cauchy stress tensorCommon symbolsσ1.00infobox
Cauchy stress tensorDimensionL − 1 M T − 2 {\displaystyle {\mathsf {L}}^{-1}{\mathsf {M}}{\mathsf {T}}^{-2}}1.00infobox
Cauchy stress tensorIn SI base unitsPa = kg⋅m−1⋅s−21.00infobox
Cauchy stress tensorOther unitsPound per square inch (psi), bar1.00infobox
Cauchy stress tensorSI unitpascal (Pa)1.00infobox
Cauchy stress tensorrelated to Cauchy's first law of motionAccording0.60section
Cauchy stress tensorrelated to Cauchy's first law of motionCauchy0.60section
Cauchy stress tensorrelated to Cauchy's stress theorem—stress tensorThe0.60section
Cauchy stress tensorrelated to Cauchy's stress theorem—stress tensorHowever0.60section
Cauchy stress tensorrelated to Cauchy's stress theorem—stress tensorCauchy's0.60section
Cauchy stress tensorrelated to Cauchy's stress theorem—stress tensorCauchy0.60section

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