Monday, February 27, 2012

1202.5418 (Lorenzo Morini et al.)

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

Lorenzo Morini, Enrico Radi, Alexander Movchan, Natalia Movchan
The focus of the article is on analysis of skew-symmetric weight matrix
functions for interfacial cracks in two dimensional anisotropic solids. It is
shown that the Stroh formalism proves to be an efficient approach to this
challenging task. Conventionally, the weight functions, both symmetric and
skew-symmetric, can be identified as a non-trivial singular solutions of the
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, that is solved in a closed form. The proposed
general method is applied to the case of a quasi-static semi-infinite crack
propagation between two dissimilar orthotropic media: explicit expressions for
the weight matrix functions are evaluated and then used in the computation of
complex stress intensity factor corresponding to an asymmetric load acting on
the crack faces.
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