Line strain representation and shear strain representation of 3D strain states.

The strain state in 3D space is usually expressed by the conventional method of combining three linear and shear strains. Due to the obvious differences between the first two strains, it is necessary to uncover their properties when describing deformation, studying yield and failure, and developing...

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Autores principales:	Shunqun Li, Xuelei Cheng, Jianbao Fu, Lin Pan, Ran Hai
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/1a91b3b1e8234e539d601483f03794f2
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id	oai:doaj.org-article:1a91b3b1e8234e539d601483f03794f2
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spelling	oai:doaj.org-article:1a91b3b1e8234e539d601483f03794f22021-12-02T20:12:51ZLine strain representation and shear strain representation of 3D strain states.1932-620310.1371/journal.pone.0259655https://doaj.org/article/1a91b3b1e8234e539d601483f03794f22021-01-01T00:00:00Zhttps://doi.org/10.1371/journal.pone.0259655https://doaj.org/toc/1932-6203The strain state in 3D space is usually expressed by the conventional method of combining three linear and shear strains. Due to the obvious differences between the first two strains, it is necessary to uncover their properties when describing deformation, studying yield and failure, and developing test apparatus or equipment. The difficulties encountered in the above work would be greatly simplified if strain states could be expressed in a single strain form, namely including only linear or shear strains. As a start, this paper explores the meaning and nature of strain states. Then, based on the hypothesis of small deformations, two strain state expressions, the linear strain expression method (LSEM) and shear strain expression method (SSEM), were established for incompressible materials with only linear strain and shear strain as parameters respectively. Furthermore, conditions, implementation steps and specific forms for the application of SSEM in 1D, 2D and 3D strain states are obtained. As an example, two representations based on tetragonal pyramid and rotating tetrahedron are especially given. Therefore, conventional strain representation methods can be expressed as a combination of line strains in a certain direction or a combination of characteristic shear strains. The results of this paper provide a new way for understanding deformation characteristics, revealing yielding process, establishing constitutive models, and developing testing apparatus or equipment.Shunqun LiXuelei ChengJianbao FuLin PanRan HaiPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 16, Iss 11, p e0259655 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Shunqun Li Xuelei Cheng Jianbao Fu Lin Pan Ran Hai Line strain representation and shear strain representation of 3D strain states.
description	The strain state in 3D space is usually expressed by the conventional method of combining three linear and shear strains. Due to the obvious differences between the first two strains, it is necessary to uncover their properties when describing deformation, studying yield and failure, and developing test apparatus or equipment. The difficulties encountered in the above work would be greatly simplified if strain states could be expressed in a single strain form, namely including only linear or shear strains. As a start, this paper explores the meaning and nature of strain states. Then, based on the hypothesis of small deformations, two strain state expressions, the linear strain expression method (LSEM) and shear strain expression method (SSEM), were established for incompressible materials with only linear strain and shear strain as parameters respectively. Furthermore, conditions, implementation steps and specific forms for the application of SSEM in 1D, 2D and 3D strain states are obtained. As an example, two representations based on tetragonal pyramid and rotating tetrahedron are especially given. Therefore, conventional strain representation methods can be expressed as a combination of line strains in a certain direction or a combination of characteristic shear strains. The results of this paper provide a new way for understanding deformation characteristics, revealing yielding process, establishing constitutive models, and developing testing apparatus or equipment.
format	article
author	Shunqun Li Xuelei Cheng Jianbao Fu Lin Pan Ran Hai
author_facet	Shunqun Li Xuelei Cheng Jianbao Fu Lin Pan Ran Hai
author_sort	Shunqun Li
title	Line strain representation and shear strain representation of 3D strain states.
title_short	Line strain representation and shear strain representation of 3D strain states.
title_full	Line strain representation and shear strain representation of 3D strain states.
title_fullStr	Line strain representation and shear strain representation of 3D strain states.
title_full_unstemmed	Line strain representation and shear strain representation of 3D strain states.
title_sort	line strain representation and shear strain representation of 3d strain states.
publisher	Public Library of Science (PLoS)
publishDate	2021
url	https://doaj.org/article/1a91b3b1e8234e539d601483f03794f2
work_keys_str_mv	AT shunqunli linestrainrepresentationandshearstrainrepresentationof3dstrainstates AT xueleicheng linestrainrepresentationandshearstrainrepresentationof3dstrainstates AT jianbaofu linestrainrepresentationandshearstrainrepresentationof3dstrainstates AT linpan linestrainrepresentationandshearstrainrepresentationof3dstrainstates AT ranhai linestrainrepresentationandshearstrainrepresentationof3dstrainstates
_version_	1718374809258164224

Line strain representation and shear strain representation of 3D strain states.

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