Abstract: The paper investigates a problem concerning the equilibrium of a solid body containing a thin rigid inclusion and a crack. It is assumed that the body is hyperelastic, therefore, it is described within the framework of finite strain theory. One of the peculiarities of this problem is a global injectivity constraint, which prevents the body, the crack faces and the inclusion from both mutual and self penetration. First, the paper deals with the differential formulation of the problem. Next, we consider energy minimization, showing that the latter provides the weak formulation of the former. Finally, the existence of the weak solution is demonstrated through the use of the variational technique. This article is part of the theme issue ‘Non-smooth variational problems with applications in mechanics’.

Cite: Furtsev A.I. , Rudoy E.M. , Sazhenkov S.A.
On hyperelastic solid with thin rigid inclusion and crack subjected to global injectivity condition
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2024. V.382. N2277. 20240115 :1-16. DOI: 10.1098/rsta.2024.0115 WOS Scopus РИНЦ OpenAlex

Dates:

Submitted:	Feb 29, 2024
Accepted:	Apr 8, 2024
Published print:	Jul 15, 2024

Identifiers:

Web of science:	WOS:001279586200007
Scopus:	2-s2.0-85199015540
Elibrary:	68936298
OpenAlex:	W4400662022

Citing:

DB	Citing
OpenAlex	2
Scopus	2
Web of science	2
Elibrary	2

Altmetrics: