Cauchy stress tensor

Representation of mechanical stress at every point within a deformed 3D object

In continuum mechanics, the Cauchy stress tensor, also called true stress tensor or simply stress tensor, completely defines the state of stress at a point inside a material in the deformed state, placement, or configuration. The second order tensor consists of nine components and relates a unit-length direction vector e to the traction vector T(e) across an imaginary surface perpendicular to e:

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