Integral identities for a semi-infinite interfacial crack in anisotropic elastic bimaterials

TL;DR

This paper develops integral identities for analyzing semi-infinite interfacial cracks in anisotropic elastic bimaterials, enabling advanced fracture mechanics analysis in complex materials and multifield theories.

Contribution

It introduces symmetric and skew-symmetric weight functions and formulates singular integral equations for interfacial cracks in anisotropic media, expanding analytical tools in fracture mechanics.

Findings

Provides a compact integral formulation for crack problems

Enables analysis of complex anisotropic and heterogeneous materials

Facilitates coupling with multifield physical phenomena

Abstract

The focus of the article is on the analysis of a semi-infinite crack at the interface between two dissimilar anisotropic elastic materials, loaded by a general asymmetrical system of forces acting on the crack faces. Recently derived symmetric and skew-symmetric weight function matrices are introduced for both plane strain and antiplane shear cracks, and used together with the fundamental reciprocal identity (Betti formula) in order to formulate the elastic fracture problem in terms of singular integral equations relating the applied loading and the resulting crack opening. The proposed compact formulation can be used to solve many problems in linear elastic fracture mechanics (for example various classic crack problems in homogeneous and heterogeneous anisotropic media, as piezoceramics or composite materials). This formulation is also fundamental in many multifield theories, where the elastic problem is coupled with other concurrent physical phenomena.