Singular invariant integrals for elastic body with delaminated thin elastic inclusion

Khludnev, A.

doi:10.1090/S0033-569X-2014-01355-9

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
MathSciNet review: 3291824
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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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