Singular path-independent energy integrals for elastic bodies with thin elastic inclusions

All-Russian conference on Nonlinear Waves: Theory and New Applications

Shcherbakov, V.V.^1,2

Lavrentyev Institute of Hydrodynamics, Novosibirsk

630090, Russia^1

Novosibirsk State University, Novosibirsk

630090, Russia^2

关键词: Elastic inclusion;    Equilibrium problem;    Euler Bernoulli beam theory;    Explicit formula;    First derivative;    Interfacial cracks;    Linear elastic bodies;    Path-independent integrals;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/722/1/012047/pdf
DOI  :  10.1088/1742-6596/722/1/012047

来源: IOP

【 摘 要 】

An equilibrium problem for a two-dimensional homogeneous linear elastic body containing a thin elastic inclusion and an interfacial crack is considered. The thin inclusion is modeled within the framework of Euler-Bernoulli beam theory. An explicit formula for the first derivative of the energy functional with respect to the crack perturbation along the interface is presented. It is shown that the formulas for the derivative associated with translation and self-similar expansion of the crack are represented as path-independent integrals along smooth contour surrounding one or both crack tips. These path-independent integrals consist of regular and singular terms and are analogs of the well-known Eshelby-Cherepanov-Rice J-integral and Knowles-Sternberg M-integral.