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The focus of the article is on analysis of skew-symmetric weight matrixfunctions for interfacial cracks in two dimensional anisotropic solids. It isshown that the Stroh formalism proves to be an efficient approach to thischallenging task. Conventionally, the weight functions, both symmetric andskew-symmetric, can be identified as a non-trivial singular solutions of thehomogeneous boundary value problem for a solid with a crack. For asemi-infinite crack, the problem can be reduced to solving a matrix Wiener-Hopffunctional equation. Instead, the Stroh matrix representation of displacementsand tractions, combined with a Riemann-Hilbert formulation, is used to obtainan algebraic eigenvalue problem, that is solved in a closed form. The proposedgeneral method is applied to the case of a quasi-static semi-infinite crackpropagation between two dissimilar orthotropic media: explicit expressions forthe weight matrix functions are evaluated and then used in the computation ofcomplex stress intensity factor corresponding to an asymmetric load acting onthe crack faces.

Stroh formalism in analysis of skew-symmetric and symmetric weight functions for interfacial cracks