These stress measures refer force or area to the reference configuration. Different index-order conventions distinguish a first Piola-Kirchhoff stress tensor from its transposed nominal stress tensor. The second Piola-Kirchhoff stress tensor has two material indices.
The second tensor has two material indices and is symmetric when the Cauchy stress tensor is symmetric. The displayed relation uses the material-first nominal stress tensor convention. In particular, is generally not this tensor. These conventions agree with A. F. Bower's definitions of stress measures.
Here the convention places the material index first: . Its stress power per reference volume is . It is the transpose of the first Piola-Kirchhoff stress tensor; some texts instead call that first tensor itself nominal stress.

Ancestors (6)

  1. Stress
  2. Constitutive equation
  3. Continuum mechanics
  4. Branches of physics
  5. Physics
  6. Home

Synonyms (1)

View article source

Discussion (0)

New discussion

There are no discussions about this article yet.

Articles by others on the same topic (1)

Piola–Kirchhoff stress tensors by Wikipedia Bot 1
View more
The Piola-Kirchhoff stress tensors are mathematical constructs used in the field of continuum mechanics to describe the state of stress in a deformable body. They provide a way to relate the stresses in a material to its deformation, capturing both the current configuration and the reference (or undeformed) configuration of the material.
Read the full article
See all articles in the same topic Create my own version