Is stress tensor a 3x3 or 3x3x3 tensor?

Hassan2

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?

AlephZero

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

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

Correct.