Abstract
In classical continuum mechanics a state of pure shear is defined as one for which there is some orthonormal basis relative to which the normal components of the Cauchy stress tensor vanish. An equivalent characterization is that the trace of the Cauchy stress tensor must vanish. We give an elementary but complete discussion of this fundamental theorem here from both the geometric and algebraic points of view.
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References
M.E. Gurtin, The linear theory of elasticity. Flügge's Handbuch der Physik,VIa/2. Berlin-Heidelberg-New York: Springer-Verlag (1972).
A.E.H. Love, A Treatise on the Mathematical Theory of Elasticity, 4th edn., Cambridge University Press (1927).
A.J. McConnel, Application of Tensor Analysis. Dover Publications Inc., New York (1957).
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Bělík, P., Fosdick, R. The State of Pure Shear. Journal of Elasticity 52, 91–98 (1998). https://doi.org/10.1023/A:1007500316569
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DOI: https://doi.org/10.1023/A:1007500316569