Cauchy's stress hypothesis

The contact traction on an oriented material cut is assumed to depend locally on the point, time and unit normal, with no independent dependence on the cut's curvature or global geometry. Together with local momentum balance and regularity sufficient for shrinking-volume arguments, this implies linear normal dependence through a stress tensor. Referential traction is measured per reference area and yields the first Piola-Kirchhoff stress tensor; spatial traction is measured per current area and yields the Cauchy stress tensor. These are different representations and the nominal tensor is not generally symmetric.