Further Study on Pure Shear |
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Authors: | T C T Ting |
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Institution: | (1) Division of Mechanics and Computation, Stanford University, Durand 262, Stanford, CA 94305-4040, USA |
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Abstract: | 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.
★Professor Emeritus of University of Illinois at Chicago and Consulting Professor of Stanford University. |
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Keywords: | 73B99 73C02 73C50 |
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