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Pure Shearing and Pure Distortional Deformations Are Not Equivalent

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Abstract

This paper attempts to clarify the notions of a state of pure shear stress and pure shearing deformations. Specifically, it is shown that pure shearing deformations and pure distortional deformations are not equivalent. Attention is limited to isotropic, compressible, hyperelastic materials. Differences between the distortional deformations of pure shearing, pure shear caused by tension and compression, and plane strain extension and contraction defined as pure shear by Rivlin and Saunders (Philos. Trans. R. Soc. Lond. Ser. A, Math. Phys. Sci. 243(865):251–288, 1951) are discussed. It is shown that these deformations are physically different and should not be expected to test the same features of a proposed form of the strain energy function. It is also shown that two deformations of pure shearing and two deformations of pure shear caused by tension and compression are nearly universal distortional deformations valid for all strain energy functions.

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Acknowledgements

The author would like to thank the reviewers for suggesting additional relevant papers and acknowledge helpful discussions with K Heiduschke.

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  1. Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, 32000, Haifa, Israel

    M. B. Rubin

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Rubin, M.B. Pure Shearing and Pure Distortional Deformations Are Not Equivalent. J Elast 142, 383–393 (2020). https://doi.org/10.1007/s10659-020-09798-1

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