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 an asymmetric load acting on the crack faces.

Stroh formalism in analysis of skew-symmetric and symmetric weight functions for interfacial cracks / Morini, Lorenzo; Radi, Enrico; A. B., Movchan; N. V., Movchan. - In: MATHEMATICS AND MECHANICS OF SOLIDS. - ISSN 1081-2865. - ELETTRONICO. - 18 (2):(2013), pp. 135-152. [10.1177/1081286512462299]

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

MORINI, Lorenzo;RADI, Enrico;
2013

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 an asymmetric load acting on the crack faces.
18 (2)
135
152
Stroh formalism in analysis of skew-symmetric and symmetric weight functions for interfacial cracks / Morini, Lorenzo; Radi, Enrico; A. B., Movchan; N. V., Movchan. - In: MATHEMATICS AND MECHANICS OF SOLIDS. - ISSN 1081-2865. - ELETTRONICO. - 18 (2):(2013), pp. 135-152. [10.1177/1081286512462299]
Morini, Lorenzo; Radi, Enrico; A. B., Movchan; N. V., Movchan
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/811302
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