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Fiber bundle model with highly disordered breaking thresholds.

Chandreyee Roy1, Sumanta Kundu1, S S Manna1

  • 1Satyendra Nath Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata-700098, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 15, 2015
PubMed
Summary
This summary is machine-generated.

This study examines the fiber bundle model with random fiber strengths. We found distinct critical behaviors and avalanche distributions, revealing insights into material failure dynamics.

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Area of Science:

  • Statistical Mechanics
  • Materials Science
  • Complex Systems

Background:

  • The fiber bundle model is a key tool for understanding material failure.
  • Understanding failure dynamics requires analyzing fiber strength distributions and load sharing.

Purpose of the Study:

  • To investigate the critical behavior of the fiber bundle model with power-law distributed fiber strengths.
  • To analytically and numerically study the model's response to varying parameters.

Main Methods:

  • Utilized equal load-sharing dynamics for fiber failure.
  • Employed analytical calculations and numerical simulations.
  • Analyzed power-law distributions of fiber breaking thresholds (p(b)∼b^-1).

Main Results:

  • Derived the asymptotic critical load σc(β) and its dependence on β.
  • Identified two distinct failure regimes based on β.
  • Characterized the fraction of broken fibers and avalanche size distributions (D(Δ)∼Δ^-ξ).

Conclusions:

  • The fiber bundle model exhibits rich critical behavior dependent on the fiber strength distribution.
  • Avalanche size distributions show power-law scaling with different exponents above and below a crossover size.
  • Results provide a deeper understanding of failure mechanisms in heterogeneous materials.