### Citation:

Movchan , A B , Mishuris , G & Piccolroaz , A 2009 , ' Symmetric and skew-symmetric weight functions in 2D perturbation models for semi-infinite interfacial cracks ' Journal of the Mechanics and Physics of Solids , vol 57 , no. 9 , pp. 1657-1682 . DOI: 10.1016/j.jmps.2009.05.003

### Abstract:

In this paper we address the vector problem of a 2D half-plane interfacial crack loaded by a general asymmetric distribution of forces acting on its faces. It is shown that the general integral formula for the evaluation of stress intensity factors, as well as high-order terms, requires both symmetric and skew-symmetric weight function matrices. The symmetric weight function matrix is obtained via the solution of a Wiener-Hopf functional equation, whereas the derivation of the skew-symmetric weight function matrix requires the construction of the corresponding full field singular solution. The weight function matrices are then used in the perturbation analysis of a crack advancing quasi-statically along the interface between two dissimilar media. A general and rigorous asymptotic procedure is developed to compute the perturbations of stress intensity factors as well as high-order terms.

### Description:

Piccolroaz, A; Mishuris, G; Movchan AB. Symmetric and skew-symmetric weight functions in 2D perturbation models for semi-infinite interfacial cracks. Journal of the Mechanics and Physics of Solids. 2009, 57(9), 1657-1682