How many INDEPENDENT components does the 3D stress tensor have at a po…

Question

How many INDEPENDENT components does the 3D stress tensor have at a point in equilibrium?

Accepted Answer

D. {'text': '6 — three normal (σ_xx, σ_yy, σ_zz) and three shear (σ_xy, σ_yz, σ_zx); the matrix is symmetric', 'label': 'B'}

The 3D stress tensor σ_ij is a symmetric 3×3 matrix (σ_ij = σ_ji from rotational equilibrium of an infinitesimal element). So 9 components reduce to 6 independent ones.

Answer

{'text': '3', 'label': 'A'}

Answer

{'text': '12', 'label': 'D'}

Answer

{'text': '9 — full 3×3', 'label': 'C'}