Lesson plan
Voigt notation
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 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. The notation is named after physicists Woldemar Voigt and John Nye. 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 its rank can be reduced by expressing it as a vector without loss of information: X = \begin{bmatrix} x_{11} & x_{12} \\ x_{12} & x_{22} \end{bmatrix} = \begin{bmatrix} x_{1 1} \\ x_{2 2} \\ x_{1 2} \end{bmatrix}. Voigt notation is used in materials science to simplify the representation of the rank-2 stress and strain tensors, and fourth-rank stiffness and compliance tensors.…
Article summary
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 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. The notation is named after physicists Woldemar Voigt and John Nye. 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 its rank can be reduced by expressing it as a vector without loss of information: X = \begin{bmatrix} x_{11} & x_{12} \\ x_{12} & x_{22} \end{bmatrix} = \begin{bmatrix} x_{1 1} \\ x_{2 2} \\ x_{1 2} \end{bmatrix}. Voigt notation is used in materials science to simplify the representation of the rank-2 stress and strain tensors, and fourth-rank stiffness and compliance tensors.…
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Discussion questions
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