Solid Mechanics > Theory for the Solid Mechanics User Interface > Stress-Strain Relationship

Stress-Strain Relationship
The symmetric stress tensor σ describes stress in a material:
This tensor consists of three normal stresses (σx, σy, σz) and six (or, if symmetry is used, three) shear stresses (τxy, τyz, τxz).
For large deformations and hyperelastic material models there are more than one stress measure:
Cauchy stress σ (the components are denoted sx, … in COMSOL Multiphysics) defined as force/deformed area in fixed directions not following the body. Symmetric tensor.
First Piola-Kirchhoff stress P (the components are denoted Px, … in COMSOL Multiphysics). This is an unsymmetric two-point tensor.
Second Piola-Kirchhoff stress S (the components are denoted Sx, … in COMSOL Multiphysics). This is a symmetric tensor, for small strains same as Cauchy stress tensor but in directions following the body.
The stresses relate to each other as