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- Voigt_notation abstract "In mathematics, Voigt notation or Voigt form in multilinear algebra is a way to represent a symmetric tensor by reducing its order. There are a few variants and associated names for this idea: Mandel notation, Mandel–Voigt notation and Nye notation are others found. Kelvin notation is a revival by Helbig (1994) of old ideas of Lord Kelvin. The differences here lie in certain weights attached to the selected entries of the tensor. Nomenclature may vary according to what is traditional in the field of application.For example, a 2×2 symmetric tensor X has only three distinct elements, the two on the diagonal and the other being off-diagonal. Thus it can be expressed as the vector .As another example:The stress tensor (in matrix notation) is given asIn Voigt notation it is simplified to a 6-dimensional vector:The strain tensor, similar in nature to the stress tensor -- both are symmetric second-order tensors --, is given in matrix form asIts representation in Voigt notation iswhere , , and are engineering shear strains.The benefit of using different representations for stress and strain is that the scalar invarianceis preserved.Likewise, a three-dimensional symmetric fourth-order tensor can be reduced to a 6×6 matrix.".
- Voigt_notation thumbnail Voigt_notation_Mnemonic_rule.png?width=300.
- Voigt_notation wikiPageID "1436668".
- Voigt_notation wikiPageRevisionID "541315626".
- Voigt_notation hasPhotoCollection Voigt_notation.
- Voigt_notation subject Category:Mathematical_notation.
- Voigt_notation subject Category:Solid_mechanics.
- Voigt_notation subject Category:Tensors.
- Voigt_notation type Abstraction100002137.
- Voigt_notation type Cognition100023271.
- Voigt_notation type Concept105835747.
- Voigt_notation type Content105809192.
- Voigt_notation type Idea105833840.
- Voigt_notation type PsychologicalFeature100023100.
- Voigt_notation type Quantity105855125.
- Voigt_notation type Tensor105864481.
- Voigt_notation type Tensors.
- Voigt_notation type Variable105857459.
- Voigt_notation comment "In mathematics, Voigt notation or Voigt form in multilinear algebra is a way to represent a symmetric tensor by reducing its order. There are a few variants and associated names for this idea: Mandel notation, Mandel–Voigt notation and Nye notation are others found. Kelvin notation is a revival by Helbig (1994) of old ideas of Lord Kelvin. The differences here lie in certain weights attached to the selected entries of the tensor.".
- Voigt_notation label "Notation de Voigt".
- Voigt_notation label "Notação de Voigt".
- Voigt_notation label "Voigt notation".
- Voigt_notation label "Voigtsche Notation".
- Voigt_notation label "Нотация Фойгта".
- Voigt_notation sameAs Voigtsche_Notation.
- Voigt_notation sameAs Notation_de_Voigt.
- Voigt_notation sameAs Notação_de_Voigt.
- Voigt_notation sameAs m.051f9y.
- Voigt_notation sameAs Q1411409.
- Voigt_notation sameAs Q1411409.
- Voigt_notation sameAs Voigt_notation.
- Voigt_notation wasDerivedFrom Voigt_notation?oldid=541315626.
- Voigt_notation depiction Voigt_notation_Mnemonic_rule.png.
- Voigt_notation isPrimaryTopicOf Voigt_notation.