Crack problem within the context of implicitly constituted quasi-linear viscoelasticity

Crack problem within the context of implicitly constituted quasi-linear viscoelasticity Full article

Journal

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

Output data

Year: 2019, Volume: 29, Number: 02, Pages: 355-372 Pages count : 18 DOI: 10.1142/s0218202519500118

Tags

crack problem; existence theorem; generalized solution; Implicit constitutive response; limiting small strain; monotonicity method; power-law hardening; quasi-linear viscoelasticity; variational inequality; variational theory; Volterra convolution operator

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 quasi-linear viscoelastic relation that stems from an implicit viscoelastic constitutive body containing a crack is considered. The abstract form of the response function is given first in Lp, p > 1, due to power-law hardening; second in L1 due to limiting small strain. In both the cases, sufficient conditions on admissible response functions are formulated, and corresponding existence theorems are proved rigorously based on the variational theory and using monotonicity methods. Due to the presence of a Volterra convolution operator, an auxiliary-independent variable of velocity type is employed. In the case of limiting small strain, the generalized solution of the problem is provided within the context of bounded measures and expressed by a variational inequality.

Itou H. , Kovtunenko V.A. , Rajagopal K.R.
Crack problem within the context of implicitly constituted quasi-linear viscoelasticity
Mathematical Models and Methods in Applied Sciences. 2019. V.29. N02. P.355-372. DOI: 10.1142/s0218202519500118 WOS Scopus РИНЦ OpenAlex

Web of science:	WOS:000459919800005
Scopus:	2-s2.0-85059592096
Elibrary:	38708695
OpenAlex:	W2904818943

DB	Citing
Scopus	20
OpenAlex	19
Elibrary	18
Web of science	19