Stress (source code)
= Stress
{title2=$\boldsymbol\sigma$}
{wiki}
<Stress> describes how internal <forces> are transmitted across imagined surfaces within a material. Dividing a small contact <force> by the cut's <area> gives the <traction>, a <vector> that depends on surface orientation. The <Cauchy stress tensor> $\sigma$ collects that dependence through $\mathbf t(\mathbf n)=\sigma\mathbf n$, where $\mathbf n$ is the oriented unit <normal vector>.
The part of <traction> perpendicular to a cut is <normal stress>; its tangential part is <shear stress>. For uniform axial loading, <stress> is $F/A$, measured in <pascals>, but a general three-dimensional state needs the full <tensor>. A fluid at rest has $\sigma=-pI$ in the tension-positive convention, whereas a stretched bar has a preferred loading direction. Changing the orientation of the imagined cut changes its <traction> without changing the physical loading. This is why one scalar <pressure> cannot represent every solid <stress> state.
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