Geodesic
Transformation geometry under simple shear
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 160 (2018) no. 1, pp. 196-206

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Transformation geometry under simple shear has been analyzed. For this purpose, the mathematical apparatus of the nonlinear theory of elasticity has been used. The sequence of transformations under simple shear has been investigated. Comparison with polar decomposition has been performed. The regions of compression and extension in the deformation ellipse have been determined. It has been shown that a simple shift can be represented in the form of successive actions of rotation, deformation and rotation.
Keywords: simple shear, deformation ellipse, Cauchy–Green tensor
Mots-clés : tensor of deformation gradient, polar decomposition. 
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     author = {A. M. Dumansky and M. Y. Rusin and V. I. Nepovinnykh},
     title = {Transformation geometry under simple shear},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {196--206},
     publisher = {mathdoc},
     volume = {160},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2018_160_1_a18/}
}
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A. M. Dumansky; M. Y. Rusin; V. I. Nepovinnykh. Transformation geometry under simple shear. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 160 (2018) no. 1, pp. 196-206. http://geodesic.mathdoc.fr/item/UZKU_2018_160_1_a18/