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Is stress tensor a 3x3 or 3x3x3 tensor?

by Hassan2
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Hassan2
#1
May8-12, 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?
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AlephZero
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May8-12, 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?
Hassan2
#3
May8-12, 11:37 AM
P: 409
Yes those diagrams that you mentioned. So when they write σ11 beside one of the arrows, the arrow is the force component in that defined direction andσ11 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.

AlephZero
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May8-12, 12:31 PM
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Is stress tensor a 3x3 or 3x3x3 tensor?

Quote Quote by Hassan2 View Post
So when they write σ11 beside one of the arrows, the arrow is the force component in that defined direction andσ11 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.
Correct.


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