Further Study on Pure Shear

It is known that the Cauchy stress tensor T is a pure shear when trT = 0. An elementary derivation is given for a coordinate system such that, when referred to this coordinate system, the diagonal elements of T vanish while the off-diagonal elements τ 1, τ 2, τ 3, are the pure shears. The structure of τ i (i = 1, 2, 3) depends on one non-dimensional parameter q = 54(detT)2 / [tr(T 2)]3, 0 ≤ q ≤ 1. When q = 0, one of the three τ i vanishes. A coordinate system can be chosen such that the remaining two have the same magnitude or one of the remaining two also vanishes. When q = 1, all three τ i have the same magnitude. However, there is a one-parameter family of coordinate systems that gives the same three τ i . For q ≠ 0 or 1, none of the three τ i vanishes and the three τ i in general have different magnitudes. Nevertheless, a coordinate system can be chosen such that two of the three τ i have the same magnitude.