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Is stress tensor a 3x3 or 3x3x3 tensor?by Hassan2
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#1
May812, 09:56 AM

P: 409

Hi all,
I have a fundamental question about ( mechanical) stress tensor. Stress tensor a 3x3 tensor whose 9 entries looks "scalars" but in figures, the stress is illustrated by nine "vectors". Does it mean the stress tensors is in fact a 3x3x3 tensor of scalars whose nonzero entries are ignored? 


#2
May812, 10:56 AM

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Stress and strain are definitely 3x3 tensors.
If you mean diagrams of a rectangular block with arrows attached to the faces, the arrows are showing the direction of the forces acting on the face, i.e. the components of ##\sigma \cdot \bf{n}## where ##\bf{n}## is the normal vector to the face. If you meant some other diagram, can you post a link to it? 


#3
May812, 11:37 AM

P: 409

Yes those diagrams that you mentioned. So when they write σ_{11} beside one of the arrows, the arrow is the force component in that defined direction andσ_{11} tells us about "magnitude" of the force. However it seems to be the force per unit area, otherwise the stress must be multiplied by the surface.
Thanks. 


#4
May812, 12:31 PM

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Is stress tensor a 3x3 or 3x3x3 tensor?



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