Mathematical model of delamination cracks on imperfect interfaces

A mathematical model of a crack along a thin and soft interface layer is studied in this paper. This type of interface could arise in a ceramic support that has been coated with a layer of high surface area material which contains the dispersed catalyst. Asymptotic analysis is applied to replace the interface layer with a set of effective contact conditions. We use the words imperfect interface to emphasise that the solution (the temperature or displacement field) is allowed to have a non-zero jump across the interface. Compared to classical formulations for cracks in dissimilar media (where ideal contact conditions are specified outside the crack), in our case the gradient field for the temperature (or displacement) is characterised by a weak logarithmic singularity. The scalar case for the Laplacian operator as well as the vector elasticity problem are considered. Numerical results are presented for a two-phase elastic strip containing a finite crack on an imperfect interface.