ORIGINAL ARTICLE Crack dynamics in a nonlinear lattice

Abstract A discrete two-dimensional square-cell latticewith a steadypropagating crack is considered. The lattice particles are connected by massless bonds, which obey a piecewise-linear double-humped stress–strain relation. Initially, Hooke’s law is valid as the first stable branch of the force– elongation diagram; then, as the elongation be-comes critical, the transition to the other branch occurs. Further, when the strain reaches the next critical value, the bond breaks. This transition is assumed to occur only in a line of the breaking bonds; the bonds outside the crack line are as-sumed to be in the initial branch all the time. The formulation relates to the crack propagation with a ‘damage zone ’ in front of the crack. An analyti-cal solution is presented that allows to determine the crack speed as a function of the far-field energy release rate, to find the total speed-dependent dis-sipation, and to estimate the role of the damage zone. The analytical formulation and the solution present a development of the previous ones fo