Three-field mixed formulation of elasticity model nonlinear in the mean normal stress for the problem of non-penetrating cracks in bodies

A class of models in the theory of elasticity is considered, where a material response between the linearized strain and the stress is assumed to be nonlinear with respect to the mean normal stress. The governing system is endowed with a mixed variational formulation treating the displacement, the d...

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Autores principales:	Hiromichi Itou, Victor A. Kovtunenko, Evgeny M. Rudoy
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	74B20 35J87 47J07 49J52 Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/7cae68b7a704480285774b6119ee3204
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spelling	oai:doaj.org-article:7cae68b7a704480285774b6119ee32042021-12-01T05:06:18ZThree-field mixed formulation of elasticity model nonlinear in the mean normal stress for the problem of non-penetrating cracks in bodies2666-496810.1016/j.apples.2021.100060https://doaj.org/article/7cae68b7a704480285774b6119ee32042021-09-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2666496821000261https://doaj.org/toc/2666-4968A class of models in the theory of elasticity is considered, where a material response between the linearized strain and the stress is assumed to be nonlinear with respect to the mean normal stress. The governing system is endowed with a mixed variational formulation treating the displacement, the deviatoric stress and the mean normal stress as three independent fields. The body contains an inner crack subjected to a non-penetration condition. The resulting problem is described as a pseudo-monotone variational inequality. Its well-posedness is established based on the Galerkin approximation, penalty regularization, and the existence theorem developed by Brézis.Hiromichi ItouVictor A. KovtunenkoEvgeny M. RudoyElsevierarticle74B2035J8747J0749J52Engineering (General). Civil engineering (General)TA1-2040ENApplications in Engineering Science, Vol 7, Iss , Pp 100060- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	74B20 35J87 47J07 49J52 Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	74B20 35J87 47J07 49J52 Engineering (General). Civil engineering (General) TA1-2040 Hiromichi Itou Victor A. Kovtunenko Evgeny M. Rudoy Three-field mixed formulation of elasticity model nonlinear in the mean normal stress for the problem of non-penetrating cracks in bodies
description	A class of models in the theory of elasticity is considered, where a material response between the linearized strain and the stress is assumed to be nonlinear with respect to the mean normal stress. The governing system is endowed with a mixed variational formulation treating the displacement, the deviatoric stress and the mean normal stress as three independent fields. The body contains an inner crack subjected to a non-penetration condition. The resulting problem is described as a pseudo-monotone variational inequality. Its well-posedness is established based on the Galerkin approximation, penalty regularization, and the existence theorem developed by Brézis.
format	article
author	Hiromichi Itou Victor A. Kovtunenko Evgeny M. Rudoy
author_facet	Hiromichi Itou Victor A. Kovtunenko Evgeny M. Rudoy
author_sort	Hiromichi Itou
title	Three-field mixed formulation of elasticity model nonlinear in the mean normal stress for the problem of non-penetrating cracks in bodies
title_short	Three-field mixed formulation of elasticity model nonlinear in the mean normal stress for the problem of non-penetrating cracks in bodies
title_full	Three-field mixed formulation of elasticity model nonlinear in the mean normal stress for the problem of non-penetrating cracks in bodies
title_fullStr	Three-field mixed formulation of elasticity model nonlinear in the mean normal stress for the problem of non-penetrating cracks in bodies
title_full_unstemmed	Three-field mixed formulation of elasticity model nonlinear in the mean normal stress for the problem of non-penetrating cracks in bodies
title_sort	three-field mixed formulation of elasticity model nonlinear in the mean normal stress for the problem of non-penetrating cracks in bodies
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/7cae68b7a704480285774b6119ee3204
work_keys_str_mv	AT hiromichiitou threefieldmixedformulationofelasticitymodelnonlinearinthemeannormalstressfortheproblemofnonpenetratingcracksinbodies AT victorakovtunenko threefieldmixedformulationofelasticitymodelnonlinearinthemeannormalstressfortheproblemofnonpenetratingcracksinbodies AT evgenymrudoy threefieldmixedformulationofelasticitymodelnonlinearinthemeannormalstressfortheproblemofnonpenetratingcracksinbodies
_version_	1718405550607171584

Three-field mixed formulation of elasticity model nonlinear in the mean normal stress for the problem of non-penetrating cracks in bodies

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