Investigation of implicit constitutive relations in which both the stress and strain appear linearly, adjacent to non-penetrating cracks

Investigation of implicit constitutive relations in which both the stress and strain appear linearly, adjacent to non-penetrating cracks Full article

Journal

Mathematical Models and Methods in Applied Sciences
ISSN: 0218-2025

Output data

Year: 2022, Volume: 32, Number: 07, Pages: 1475-1492 Pages count : 18 DOI: 10.1142/s0218202522500336

Tags

blow-up; crack; implicit constitutive response; non-penetration condition; Nonlinear elasticity; regularization; variational inequality; well-posedness analysis

Authors

Itou Hiromichi ² , Kovtunenko Victor A. ^1,3 , Rajagopal Kumbakonam R. ⁴

Affiliations

1	Lavrentyev Institute of Hydrodynamics, Siberian Division of the Russian Academy of Sciences
2	Department of Mathematics, Tokyo University of Science
3	Institute for Mathematics and Scientific Computing, University of Graz
4	Department of Mechanical Engineering, Texas A&M University, College Station, Texas 77843, USA

A novel class of implicit constitutive relations is studied, wherein the stress and the linearized strain appear linearly, that describe material response in elastic porous bodies like rocks, ceramics, concrete, cement, bones and metals. The constitutive relation is applied to a body with a crack subjected to non-penetration conditions between the opposite crack faces. To treat well-posedness of a corresponding variational inequality, we rely on a new approximation by thresholding dilatation and apply the Lions existence theorem on pseudo-monotone variational inequalities. An analytical solution to a specific example (without crack) under uniform triaxial loading is constructed, wherein blow-up can take place at a finite load, and this difficulty is overcome within a thresholding approximation so that blow-up does not occur.

Itou H. , Kovtunenko V.A. , Rajagopal K.R.
Investigation of implicit constitutive relations in which both the stress and strain appear linearly, adjacent to non-penetrating cracks
Mathematical Models and Methods in Applied Sciences. 2022. V.32. N07. P.1475-1492. DOI: 10.1142/s0218202522500336 WOS Scopus РИНЦ OpenAlex

Web of science:	WOS:000829656100005
Scopus:	2-s2.0-85132973942
Elibrary:	49150487
OpenAlex:	W4288047618

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Scopus	8
OpenAlex	8
Elibrary	8
Web of science	8