Piola–Kirchhoff stress tensors

In the case of finite deformations, the Piola–Kirchhoff stress tensors (named for Gabrio Piola and Gustav Kirchhoff) express the stress relative to the reference configuration. This is in contrast to the Cauchy stress tensor which expresses the stress relative to the present configuration.

Source: Wikipedia — Piola–Kirchhoff stress tensors (CC BY-SA 4.0)