TY - JOUR

T1 - Singular path-independent energy integrals for elastic bodies with Euler–Bernoulli inclusions

AU - Khludnev, Alexander M.

AU - Shcherbakov, Viktor V.

PY - 2017/11/1

Y1 - 2017/11/1

N2 - This paper is devoted to a rigorous analysis of an equilibrium problem for a two-dimensional homogeneous anisotropic elastic body containing a thin isotropic elastic inclusion. The thin inclusion is modelled within the framework of Euler–Bernoulli beam theory. Partial delamination of the inclusion from the elastic body results in the appearance of an interfacial crack. We deal with nonlinear conditions that do not allow the opposing crack faces to penetrate each other. We derive a formula for the first derivative of the energy functional with respect to the regular crack perturbation along the interface, which is related to energy release rates. It is proved that the energy release rates associated with crack translation and self-similar expansion are represented as path-independent integrals along smooth curves surrounding one or both crack tips. The path-independent integrals consist of regular and singular terms and are analogues of the well-known Eshelby–Cherepanov–Rice J-integral and Knowles–Sternberg M-integral.

AB - This paper is devoted to a rigorous analysis of an equilibrium problem for a two-dimensional homogeneous anisotropic elastic body containing a thin isotropic elastic inclusion. The thin inclusion is modelled within the framework of Euler–Bernoulli beam theory. Partial delamination of the inclusion from the elastic body results in the appearance of an interfacial crack. We deal with nonlinear conditions that do not allow the opposing crack faces to penetrate each other. We derive a formula for the first derivative of the energy functional with respect to the regular crack perturbation along the interface, which is related to energy release rates. It is proved that the energy release rates associated with crack translation and self-similar expansion are represented as path-independent integrals along smooth curves surrounding one or both crack tips. The path-independent integrals consist of regular and singular terms and are analogues of the well-known Eshelby–Cherepanov–Rice J-integral and Knowles–Sternberg M-integral.

KW - crack

KW - energy release rates

KW - Euler–Bernoulli beam

KW - J-integral

KW - M-integral

KW - nonpenetration conditions

KW - shape derivative of energy functional

KW - variational inequality

UR - http://www.scopus.com/inward/record.url?scp=85032983064&partnerID=8YFLogxK

U2 - 10.1177/1081286516664208

DO - 10.1177/1081286516664208

M3 - Article

AN - SCOPUS:85032983064

VL - 22

SP - 2180

EP - 2195

JO - Mathematics and Mechanics of Solids

JF - Mathematics and Mechanics of Solids

SN - 1081-2865

IS - 11

ER -