Elastoplastic Depinning: Avalanche Statistics

Amorphous solids yield through avalanches with mean-field exponent — stress drops distributed as s^{−3/2}.

L = 16
γ̇ = 0.005
α = 0.40
Total stress τ =  |  Avalanche size =  |  Total avalanches = 0  |  Max avalanche = 0
Elastoplastic model (Picard et al 2002, Lin et al 2014): each site has a local stress threshold τ_c drawn from P(τ).
When τ_i > τ_c,i the site yields: τ_i → new random value, and redistributes α/(L²−1) to all others.
Mean-field avalanche statistics: P(s) ~ s^{-τ} with τ = 3/2 at depinning threshold.
Grid colors: local stress (dark = low, gold = near-yield, red = yielding). Log-log histogram shows power law.