Propagation of Slepyan's crack in a non-uniform elastic lattice

We model and derive the solution for the problem of a Mode I semi-infinite crack propagating in a discrete triangular lattice with bonds having a contrast in stiffness in the principal lattice directions. The corresponding Green's kernel is found and from this wave dispersion dependencies are obtained in explicit form. An equation of the Wiener-Hopf type is also derived and solved along the crack face, in order to compute the stress intensity factor for the semi-infinite crack. The crack stability is analysed via the evaluation of the energy release rate for different contrasts in stiffness of the bonds.