## 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.

### MSC:

 74A05 Kinematics of deformation 74A10 Stress

### Keywords:

pure shear; stress tensor; orthogonal projector
Full Text: