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

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

Journal

Applications in Engineering Science
ISSN: 2666-4968

Output data

Year: 2021, Volume: 7, Pages: 100060 Pages count : 5 DOI: 10.1016/j.apples.2021.100060

Tags

Contact; Crack; Mixed variational formulation; Nonlinear elasticity; Penalization; Pseudo-monotone variational inequality; Quasi-linear elliptic problem; Volumetric-deviatoric decomposition; Well-posedness

Authors

Itou Hiromichi ¹ , Kovtunenko Victor A. ^2,3 , Rudoy Evgeny M. ³

Affiliations

1	Tokyo University of Science
2	University of Graz
3	Lavrentyev Institute of Hydrodynamics

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.

Itou H. , Kovtunenko V.A. , Rudoy E.M.
Three-field mixed formulation of elasticity model nonlinear in the mean normal stress for the problem of non-penetrating cracks in bodies
Applications in Engineering Science. 2021. V.7. P.100060. DOI: 10.1016/j.apples.2021.100060 WOS Scopus РИНЦ OpenAlex

Published print:

Sep 30, 2021

Web of science:	WOS:001025476000010
Scopus:	2-s2.0-85136012890
Elibrary:	60780235
OpenAlex:	W3177495628

DB	Citing
Scopus	5
OpenAlex	4
Elibrary	1
Web of science	5