1210.0989 (Ashivni Shekhawat et al.)

From damage percolation to crack nucleation through finite size
criticality    [PDF]

Ashivni Shekhawat, Stefano Zapperi, James P. Sethna

We present a unified theory of fracture in disordered brittle media that reconciles apparently conflicting results reported in the literature. Our renormalization group based approach yields a phase diagram in which the percolation fixed point, expected for infinite disorder, is unstable for finite disorder and flows to a zero-disorder nucleation-type fixed point, thus showing that fracture has mixed first order and continuous character. In a region of intermediate disorder and finite system sizes, we predict a crossover with mean-field avalanche scaling. We discuss intriguing connections to other phenomena where critical scaling is only observed in finite size systems and disappears in the thermodynamic limit.

View original: http://arxiv.org/abs/1210.0989