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

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 δ − 10 {\delta ^{ - 10}} are derived for the stress intensity factors and the crack energy, where 2 δ 2\delta denotes the width of the strip and δ \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.