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.
Similar content being viewed by others
References
M. Gurtin, The linear theory of elasticity. Flugge’s Handbuch der physik, Via/2. Springer, Berlin Heidelberg New York (1972).
P. Belik and R. Fosdick, The state of pure shear. J. Elast. 52 (1998) 91–98.
Ph. Boulanger and M. Hayes, On pure shear. J. Elast. 77 (2004) 83–89.
I. S. Sokolnikoff, Mathematical Theory of Elasticity. McGraw Hill, New York (1983).
M. Hayes, A note on maximum orthogonal shear stress and shear strain. J. Elast. 21 (1989) 117–120.
Author information
Authors and Affiliations
Corresponding author
Additional information
★Professor Emeritus of University of Illinois at Chicago and Consulting Professor of Stanford University.
Rights and permissions
About this article
Cite this article
Ting, T.C.T. Further Study on Pure Shear. J Elasticity 83, 95–104 (2006). https://doi.org/10.1007/s10659-005-9041-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10659-005-9041-1