In continuum mechanics, the Cauchy stress tensor σ {\displaystyle {\boldsymbol {\sigma }}} , true stress tensor,[1] or simply called the stress tensor is a second order tensor named after Augustin-Louis Cauchy. The tensor consists of nine components σ i j {\displaystyle \sigma _{ij}} that completely define the state of stress at a point inside a material in the deformed state, placement, or configuration. The tensor relates a unit-length direction vector n to the stress vector T(n) across an imaginary surface perpendicular to n: