Piola-Kirchhoff stress

The Piola-Kirchhoff stress is a concept in the mechanics of solids that relates stress and strain within a material. It is part of a larger framework that includes Newtonian equations of motion, the geometry of deformation, and material-specific stress-strain relationships.1234

There are two main types of Piola-Kirchhoff stress tensors:
* First Piola-Kirchhoff stress: This tensor describes the force per unit of original area acting on a deformed body.2
* Second Piola-Kirchhoff stress: This tensor is used when considering finite elastic deformations, particularly in materials like rubber where strains can be large. It is related to the free energy of the material and the strain measure.2

These concepts are crucial for understanding how materials deform and respond to applied forces, especially in scenarios involving large deformations or complex material behaviors like viscoelasticity and plasticity.24