4.2(b)  Stress Tensor    (Cont.)

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Let   be a tensor at point P. The infinitesimal cube is drawn with P at the center of the box. The three faces have unit normal (1,0,0),(0,1,0) and (0,0,1) with unit area.

Let  be the stress vector for , and

be the stress vector for , and

be the stress vector for  , then  

Consider any one of the stress vector; then in general,

  and      or   

Thus

is the stress tensor with the first subscript in , Subscript  indicates normal to  the plane and  indicates the direction.

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