At any given point p of a continuous medium

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At any given point P of a continuous medium, the surface forces are given by the stress tensor, which is a real symmetric matrix Σ. It is a well-known theorem of linear algebra (see the appendix) that any such matrix can be brought into diagonal form by a suitable rotation of the Cartesian coordinate axes. Use this to prove that at any point P there are three orthogonal directions (the principal stress axes at P) with the property that the surface force on any surface normal to one of these directions is exactly normal to the surface.

Reference no: EM131049781

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