On the state of pure shear. (English) Zbl 1289.74003

The Cauchy stress tensor in the three-dimensional Euclidian space is in state of pure shear if there exists an orthogonal basis such that the normal components of the stress tensor in that basis vanish. A characterization of pure shear is given by the so-called fundamental theorem: the stress is in state of pure shear if and only if the stress tensor is traceless. A new, very elegant proof of this theorem is presented. It is shown that the state of pure shear is the same for all singular symmetric traceless tensors in \(\mathrm E^3\), up to rotation. The fundamental theorem for pure shear state in the \(n\)-dimensional Euclidian space is also proved.


74A05 Kinematics of deformation
74A10 Stress
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