Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Singular invariant integrals for elastic body with delaminated thin elastic inclusion

Author: A. M. Khludnev
Journal: Quart. Appl. Math. 72 (2014), 719-730
MSC (2010): Primary 35J50, 35J55, 35J40
DOI: https://doi.org/10.1090/S0033-569X-2014-01355-9
Published electronically: October 17, 2014
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Abstract: We consider an equilibrium problem for a $ 2D$ elastic body with a thin elastic inclusion. It is assumed that the inclusion is partially delaminated, therefore providing the presence of a crack. Inequality type boundary conditions are imposed at the crack faces to prevent a mutual penetration of the faces. Differentiability properties of the energy functional with respect to the crack length are analyzed. We prove an existence of the derivative and find a formula for this derivative. It is shown that the formula for the derivative can be written in the form of a singular invariant integral.

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Additional Information

A. M. Khludnev
Affiliation: Lavrentyev Institute of Hydrodynamics of the Russian Academy of Sciences and Novosibirsk State University, Novosibirsk 630090, Russia
Email: khlud@hydro.nsc.ru

DOI: https://doi.org/10.1090/S0033-569X-2014-01355-9
Keywords: Thin inclusion, crack, non-linear boundary conditions, non-penetration, variational inequality, derivative of energy functional, invariant integral
Received by editor(s): November 22, 2012
Published electronically: October 17, 2014
Article copyright: © Copyright 2014 Brown University

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