Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Plane-strain problem of two coplanar cracks in an initially stressed neo-Hookean elastic layer

Authors: Ranjit S. Dhaliwal and Brij Mohan Singh
Journal: Quart. Appl. Math. 36 (1979), 361-376
DOI: https://doi.org/10.1090/qam/99639
MathSciNet review: QAM99639
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Abstract: We consider the problem of determining the stress intensity factors and the crack energy in an infinitely long strip of an initially stressed neo-Hookean elastic material containing two coplanar Griffith cracks. We assume that the cracks are opened by a constant internal pressure and that the edges of the strip are either rigidly fixed or stress-free. By the use of Fourier transforms we reduce the problem to solving a set of triple integral equations with cosine kernel and a weight function. These equations are reduced to a Fredholm integral equation of the second kind by using finite Hilbert transform technique. Analytical expressions up to the order $ {\delta ^{ - 10}}$ are derived for the stress intensity factors and the crack energy, where $ 2\delta $ denotes the width of the strip and $ \delta $ is much greater than 1. Numerical values of the stress intensity factors and the crack energy are graphed to display the effect of initial stress.

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DOI: https://doi.org/10.1090/qam/99639
Article copyright: © Copyright 1979 American Mathematical Society

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