Euclidean geometry | Tensors

Two-point tensor

Two-point tensors, or double vectors, are tensor-like quantities which transform as Euclidean vectors with respect to each of their indices. They are used in continuum mechanics to transform between reference ("material") and present ("configuration") coordinates. Examples include the deformation gradient and the first Piola–Kirchhoff stress tensor. As with many applications of tensors, Einstein summation notation is frequently used. To clarify this notation, capital indices are often used to indicate reference coordinates and lowercase for present coordinates. Thus, a two-point tensor will have one capital and one lower-case index; for example, AjM. (Wikipedia).

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Mixed tensor | Piola–Kirchhoff stress tensor | Covariance and contravariance of vectors | Tensor product | Euclidean vector | Deformation gradient | Tensor