Transformation geometry under simple shear
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 region...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2018-03-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
| Subjects: | |
| Online Access: | https://kpfu.ru/transformation-geometry-under-simple-shear_342792.html |
| _version_ | 1826908181105737728 |
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| author | A.M. Dumansky M.Y. Rusin V.I. Nepovinnykh |
| author_facet | A.M. Dumansky M.Y. Rusin V.I. Nepovinnykh |
| author_sort | A.M. Dumansky |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T16:02:28Z |
| format | Article |
| id | doaj.art-3f6b0437ec3c40a3b5135f82f9ec8dd0 |
| institution | Directory Open Access Journal |
| issn | 2541-7746 2500-2198 |
| language | English |
| last_indexed | 2025-02-17T09:18:37Z |
| publishDate | 2018-03-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj.art-3f6b0437ec3c40a3b5135f82f9ec8dd02025-01-02T13:08:32ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982018-03-011601196206Transformation geometry under simple shearA.M. Dumansky0M.Y. Rusin1V.I. Nepovinnykh2Mechanical Engineering Research Institute, Russian Academy of Sciences, Moscow, 101990 RussiaAO ORPE Technologiya, Obninsk, 249031 RussiaAO ORPE Technologiya, Obninsk, 249031 RussiaTransformation 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.https://kpfu.ru/transformation-geometry-under-simple-shear_342792.htmlsimple sheardeformation ellipsetensor of deformation gradientcauchy–green tensorpolar decomposition |
| spellingShingle | A.M. Dumansky M.Y. Rusin V.I. Nepovinnykh Transformation geometry under simple shear Учёные записки Казанского университета: Серия Физико-математические науки simple shear deformation ellipse tensor of deformation gradient cauchy–green tensor polar decomposition |
| title | Transformation geometry under simple shear |
| title_full | Transformation geometry under simple shear |
| title_fullStr | Transformation geometry under simple shear |
| title_full_unstemmed | Transformation geometry under simple shear |
| title_short | Transformation geometry under simple shear |
| title_sort | transformation geometry under simple shear |
| topic | simple shear deformation ellipse tensor of deformation gradient cauchy–green tensor polar decomposition |
| url | https://kpfu.ru/transformation-geometry-under-simple-shear_342792.html |
| work_keys_str_mv | AT amdumansky transformationgeometryundersimpleshear AT myrusin transformationgeometryundersimpleshear AT vinepovinnykh transformationgeometryundersimpleshear |