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

TL;DR

This paper models a Mode I crack propagating in a non-uniform elastic lattice, deriving explicit solutions for wave dispersion, stress intensity, and stability analysis considering bond stiffness contrasts.

Contribution

It introduces a novel analytical framework for crack propagation in non-uniform lattices, including explicit Green's functions and stability criteria.

Findings

Explicit wave dispersion relations derived

Stress intensity factors computed for various stiffness contrasts

Crack stability analyzed through energy release rate

Abstract

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.