Definition of Various Tensor Orders

A scalar is a tensor of order zero and has 3° = 1 component. Because it has only magnitude and not direction, no transformation relations are needed. Examples of scalars include speed (but not velocity), work, and energy. 

A vector is a tensor of first order and has 3 = 3 components. Vectors transform according to 

Stress and strain are both second-order tensors. 

The stiffness and compliances in stress-strain and strain-stress relations are fourth-order tensors because they relate two second-order tensors  

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