Statistical model of material failure — avalanches and critical point
80
2.0
0.010
Total load F: 0.000
Intact fibers: --
Broken: 0
Last avalanche: 0
Peak load: --
Status: Ready
Physics
The fiber bundle model (Daniels 1945, Peirce 1926) considers N parallel fibers, each failing when stress exceeds a random threshold drawn from a distribution. Two sharing rules: Equal Load Sharing (ELS/mean field) — load from broken fibers redistributes equally; Local Load Sharing (LLS) — overloads neighbors, causing crack propagation. ELS has an exact critical point: the bundle fails catastrophically at a universal peak load. Failure statistics show power-law avalanche distributions: P(s) ~ s^{-5/2} (ELS), related to critical percolation.