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

Morini, Lorenzo ORCID: https://orcid.org/0000-0001-7155-5036, 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:	21 Oct 2022 06:54
URI:	https://orca.cardiff.ac.uk/id/eprint/98723

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