Cauchystresstensor
The Cauchy stress tensor, denoted sigma, is a second-order tensor that relates the traction vector on a plane to the plane’s unit normal in the current (deformed) configuration of a continuum. For a plane with unit normal n, the traction (force per unit area) acting on that plane is t = sigma · n. Its components sigma_ij describe the state of stress at a material point.
In standard (non-polar) continuum mechanics, the Cauchy stress tensor is symmetric: sigma = sigma^T. This symmetry follows
The Cauchy stress is defined in the current configuration. In finite deformation, it is related to other
Practically, the Cauchy stress is determined from traction measurements and constitutive models, and it is central