Avalanche Dynamics of Crack Propagation and Contact Line Depinning

A model for crack propagation and contact line depinning is studied. Although the model contains nonlocal interactions, it obeys general scaling relations for depinning via localized bursts or avalanches. Our numerical result for the roughness exponent in one dimension, $\chi=0.49 \pm 0.05$, agrees with recent experiments on cracks measuring the in-plane roughness $\chi \simeq 0.5 - 0.6$, as well as mean field arguments giving $\chi=1/2$, but is significantly higher than the functional renormalization group prediction $\chi = 1/3$.