The interface crack under combined loading: an eigenvalue problem for the gap

Abstract

To avoid the difficulty of overlapping material near the crack tips, the tips of the crack are assumed to be closed (the Comninou model). The exact series solution to the problem of the interface crack under combined loading is complicated, and it is difficult to take advantage of the smallness of the left contact zone to obtain simple asymptotic approximations to the quantities of physical interest. Here, the gap is shown to satisfy an eigenvalue problem. The method of matched inner and outer expansions is used to obtain a simple uniform approximation to this quantity. Similar results are obtained for the tangential shift, which satisfies the same differential equation as the gap. The tractions at the interface also satisfy a second order differential equation and simple uniform approximations are obtained for these quantities.