Why is the stress tensor SYMMETRIC (σ_xy = σ_yx, etc.)?

Question

Accepted Answer

C. {'text': 'By moment-equilibrium of an infinitesimal cube — unmatched shears would cause rotation', 'label': 'B'}

Consider an infinitesimal cube. The shear stress σ_xy on the +x face creates a torque about z. For ω_z = 0 (no spin), an equal-and-opposite torque from σ_yx on the +y face must balance ⇒ σ_xy = σ_yx. Same for all pairs.

Answer

{'text': 'By isotropy', 'label': 'D'}

Answer

{'text': "By Hooke's law", 'label': 'A'}

Answer

{'text': 'By symmetry of the strain tensor', 'label': 'C'}