The Cauchy's stress quadric, also called the " stress surface ", is a surface of the second order that traces the variation of the normal stress vector \ sigma _ \ mathrm n \, \ ! as the orientation of the planes passing through a given point is changed.
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The reduced stress tensor is a mathematical computation approach to determining the three principal axes and the stress ratio, totally four independent unknowns, calculated as eigenvectors and eigenvalue respectively, so that this method is more complete and accurate than the mentioned graphical approaches . Nine stress vectors acting on a cube ( point ), in which ? 11, ? 22 and ? 33 are the principal axes
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The "'Euler Cauchy stress principle "'states that " upon any surface ( real or imaginary ) that divides the body, the action of one part of the body on the other is equivalent ( equipollent ) to the system of distributed forces and couples on the surface dividing the body ", and it is represented by a field \ mathbf { T } ^ { ( \ mathbf { n } ) }, called the stress vector, defined on the surface S and assumed to depend continuously on the surface's unit vector \ mathbf n.
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