Nonlinear elasticity with limiting small strain for cracks subject to non-penetration

A major drawback of the study of cracks within the context of the linearized theory of elasticity is the inconsistency that one obtains with regard to the strain at a crack tip, namely it becoming infinite. In this paper we consider the problem within the context of an elastic body that exhibits lim...

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Published inMathematics and mechanics of solids Vol. 22; no. 6; pp. 1334 - 1346
Main Authors Itou, Hiromichi, Kovtunenko, Victor A, Rajagopal, Kumbakonam R
Format Journal Article
LanguageEnglish
Published London, England SAGE Publications 01.06.2017
Subjects
limiting small strain
regularization
penalization
nonlinear crack with non-penetration
variational inequality
Nonlinear elasticity
generalized solution
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Summary:A major drawback of the study of cracks within the context of the linearized theory of elasticity is the inconsistency that one obtains with regard to the strain at a crack tip, namely it becoming infinite. In this paper we consider the problem within the context of an elastic body that exhibits limiting small strain wherein we are not faced with such an inconsistency. We introduce the concept of a non-smooth viscosity solution which is described by generalized variational inequalities and coincides with the weak solution in the smooth case. The well-posedness is proved by the construction of an approximation problem using elliptic regularization and penalization techniques.
ISSN:1081-2865
1741-3028
DOI:10.1177/1081286516632380