Mathematical modelling of the interface crack. A new improved numerical method

A pre-stressed fiber elastic composite containing an anti-plane interface crack is considered. The boundary conditions of our problem are leading to a homogeneous and a non-homogeneous problem. Using the theory of Cauchy’s integral ( [1–4]), Guz’s representation ( [1,3]) and the numerical analysis we determine the incremental fields in the vicinity of the crack tips. In [5] we presented a numerical method for calculating the complex integrals which appear in the non-homogeneous complex differential equation for the complex potential. In the present paper we shall improve the method, providing an appropriate treatment of the singularities. We shall deliver a very good formula for calculating numerically the complex integrals employing Plemelj’s fomulas and Cauchy’s integral. A numerical example regarding the propagation of an anti-plane interface crack in glass-epoxy is studied.