Cauchy stress tensor

Summary

The Cauchy stress tensor $\sigma$ at a point of a deformed body is a linear map. It sends the unit normal $n$ of a surface element to the traction $\sigma n$ across that element. Its nine components in a basis give the stress on the three coordinate planes and determine the stress on every other plane. It is symmetric, by balance of angular momentum, and it is the true stress, measured per unit area of the deformed body.