 Solution

Choose the outward unit normal $n$ to the boundary of the chosen current material subbody. The traction $t(x,n)$ is the contact force exerted on that subbody per unit current area at the boundary point. Reversing the subbody side reverses $n$ and $t$.

By Cauchy's stress theorem, the dependence on $n$ is linear. With the usual column-vector convention the Cauchy stress tensor satisfiesThe same point has different traction vectors on differently oriented planes, but a single Cauchy stress tensor encodes all of them. In the absence of body couples, conservation of angular momentum makes $\tau$ symmetric.