Stress

Remarks

In a fluid at rest with pressure $p$, the traction is $t(x, n) = -p(x)\, n$: the normal stress is $-p$ and the shear stress is $0$. In a bar along the first axis under a tensile force $P$ spread uniformly over the cross-section area $A$, the traction on a cross-section with $n = e_1$ is $(P/A)\, e_1$. Gravity is not a stress: it acts on the volume of the material, not across surfaces, and is described by a body force per unit mass. The assumption that $t$ depends on the surface only through its normal $n$ is Cauchy's stress principle; Cauchy's stress theorem then shows that $t$ is linear in $n$. Stress has the units of pressure, the pascal $\text{N}/\text{m}^2$.