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

Morini, Lorenzo, Radi, E., Movchan, A. and Movchan, N. 2013. Stroh formalism in analysis of skew-symmetric and symmetric weight functions for interfacial cracks. Mathematics and Mechanics of Solids 18 (2) , pp. 135-152. 10.1177/1081286512462299

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Abstract

The focus of the paper is on the analysis of skew-symmetric weight functions for interfacial cracks in two-dimensional anisotropic solids. It is shown that the Stroh formalism proves to be an efficient tool for this challenging task. Conventionally, the weight functions, both symmetric and skew-symmetric, can be identified as non-trivial singular solutions of a homogeneous boundary-value problem for a solid with a crack. For a semi-infinite crack, the problem can be reduced to solving a matrix Wiener–Hopf functional equation. Instead, the Stroh matrix representation of displacements and tractions, combined with a Riemann–Hilbert formulation, is used to obtain an algebraic eigenvalue problem, which is solved in a closed form. The proposed general method is applied to the case of a quasi-static semi-infinite crack propagating between two dissimilar orthotropic media: explicit expressions for the weight functions are evaluated and then used in the computation of the complex stress intensity factor corresponding to a general distribution of forces acting on the crack faces.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Engineering
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Uncontrolled Keywords: Interfacial crack, Riemann–Hilbert problem, Stroh formalism, weight functions, stress intensity factor
Publisher: SAGE Publications
ISSN: 1081-2865
Date of Acceptance: 1 July 2012
Last Modified: 17 Oct 2019 15:04
URI: http://orca.cf.ac.uk/id/eprint/98723

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