Random fiber bundle with many discontinuities in the threshold distribution.

Area of Science:

• Statistical mechanics
• Materials science
• Complex systems

Background:

• The random fiber bundle model (RFBM) is a key model for understanding material failure.
• Previous studies often focused on uniform or single-discontinuity threshold distributions.

Purpose of the Study:

• To investigate the breakdown behavior of an RFBM with n discontinuities in its threshold distribution.
• To analyze the impact of multiple threshold gaps on critical exponents and avalanche size distributions.

Main Methods:

• Utilized a global load sharing scheme for fiber failure.
• Defined n+1 fiber classes with uniform strength distributions and gaps between classes.
• Analyzed critical stress, critical exponents, and avalanche size distributions.

Main Results:

• Critical exponents are identical to those of a RFBM with a uniform distribution and global load sharing.
• Avalanche size distributions show non-universal, non-power-law behavior for small sizes, especially near critical distribution.
• Behavior for arbitrary n is qualitatively similar to the n=1 case.

Conclusions:

• The critical exponents in this multi-discontinuity RFBM are robust and independent of the number of discontinuities.
• Avalanche size distribution complexity arises from the interplay of multiple threshold classes.
• The model provides insights into failure mechanisms in heterogeneous materials.