Avalanche-size distributions in mean-field plastic yielding models.

Area of Science:

• Condensed Matter Physics
• Materials Science
• Statistical Mechanics

Background:

• Amorphous solids exhibit avalanches during yielding.
• Mean-field models like Hebraud-Lequeux describe these phenomena.
• Avalanche size distributions often follow power laws, N(S)∼S(-τ).

Purpose of the Study:

• To investigate the size distribution of avalanches in mean-field models of amorphous solids.
• To determine the exponent τ under different dynamic protocols.
• To compare findings with the depinning transition.

Main Methods:

• Analysis of mean-field models (Hebraud-Lequeux).
• Examination of avalanche size distribution N(S).
• Comparison of random triggering versus quasistatic strain protocols.

Main Results:

• The exponent τ depends on the dynamic protocol.
• Random triggering yields τ=3/2, consistent with mean-field and depinning models.
• Quasistatic strain loading results in a smaller exponent, near 1.

Conclusions:

• The exponent characterizing avalanche size distribution is sensitive to the loading protocol.
• A mapping to an effective random walk explains the quasistatic loading result.
• Understanding these dynamics is crucial for predicting amorphous solid failure.