Integral identities for an interfacial crack in an anisotropic bimaterial with an imperfect interface

TL;DR

This paper develops a method using weight functions to derive integral equations for an interfacial crack in anisotropic bimaterials with imperfect interfaces, and solves these equations numerically, validating results with finite element analysis.

Contribution

It introduces a novel approach combining weight functions and integral equations to analyze cracks in anisotropic bimaterials with imperfect interfaces.

Findings

Integral equations effectively model interfacial crack behavior.

Numerical solutions align well with finite element results.

Method applies to various anisotropic orientations and imperfections.

Abstract

We study a crack lying along an imperfect interface in an anisotropic bimaterial. A method is devised where known weight functions for the perfect interface problem are used to obtain singular integral equations relating the tractions and displacements for both the in-plane and out-of-plane fields. The integral equations for the out-of-plane problem are solved numerically for orthotropic bimaterials with differing orientations of anisotropy and for different extents of interfacial imperfection. These results are then compared with finite element computations.