 Cauchy stress tensor

The stress tensor maps a surface normal to the traction exerted across that surface. Its divergence is the force density in local momentum balance. For an incompressible Newtonian fluid it combines pressure with twice the viscosity times the symmetric strain-rate tensor.

The Cauchy stress tensor is a fundamental concept in continuum mechanics that describes the internal state of stress at a point within a material. It provides a way to quantify how internal forces are distributed within a material due to external loads, deformations, or other influences.