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On boundary value problems in fracture of elastic Composites

Published online by Cambridge University Press:  26 September 2008

Gennady S. Mishuris  and
Zbigniew S. Olesiak
Gennady S. Mishuris
Affiliation:
Department of Applied Mathematics and Mechanics, University of Warsaw, Poland
Zbigniew S. Olesiak
Affiliation:
Department of Applied Mathematics and Mechanics, University of Warsaw, Poland
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Abstract

We present a method of solution of a class of fracture problems in the theory of elasticity. The method can be applied to any problem reducible to Poisson's equation, e.g. heat conduction and mass diffusion in solids, theory of consolidation and the like. The novelty of the paper is that we address regions of layered composites with notches, or, in a particular case, with a crack. Within the framework of classical analysis, we apply Fourier and Mellin transforms, 'fit' them together, and reduce the problem to solving a singular integral equation with fixed singularities on a semi-axis. We show the existence and uniqueness of solutions of the equations under consideration, and justify the asymptotics necessary for applications. We show the practical usefulness of the method on the examples of an antiplane problem of fracture mechanics. From our solution, we are able to find the stress intensity factor in the case when a crack tip penetrates a layered composite consisting of 60 layers, and show the limits of applicability of the anisotropic model of such composites.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 6 , Issue 6 , December 1995 , pp. 591 - 610
Copyright
Copyright © Cambridge University Press 1995

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