Order 2 tensor in a Cartesian coordinate system

X.B.1.2 Order 2 tensor in a Cartesian coordinate system

A Cauchy stress tensor $σ$ is characterized by its components $σ_{i j}$ in the Cartesian coordinate system ${O, e_{i}}$ . (One uses the same notations as in section X.B.1.1).

σ = σ_{i j} (e_{i} \otimes e_{j}) .

The nine quantities $(e_{i} \otimes e_{j})$ can be considered as the basic tensors from which all other tensors are obtained as linear combinations. Note that the Cauchy stress tensor is always symmetrical so that $σ_{i j} = σ_{j i}$ .

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