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 collects that dependence through , where 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 , measured in pascals, but a general three-dimensional state needs the full tensor. A fluid at rest has 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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