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Phase transition in fiber bundle models with recursive dynamics.

Pratip Bhattacharyya1, Srutarshi Pradhan, Bikas K Chakrabarti

  • 1Theoretical Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Sector-1, Block-AF, Bidhannagar, Kolkata 700 064, India. pratip@cmp.saha.ernet.in

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 6, 2003
PubMed
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This study reveals a second-order phase transition in fiber bundle models. Exceeding a critical stress triggers a shift from partial to total fiber failure, with universal critical exponents observed.

Area of Science:

  • Statistical Mechanics
  • Materials Science
  • Complex Systems

Background:

  • Fiber bundle models are crucial for understanding material failure.
  • Random fiber strength distributions and global load sharing are key model assumptions.

Purpose of the Study:

  • To investigate the phase transition dynamics in fiber bundle models with random strengths.
  • To characterize the critical properties and universality of the failure process.

Main Methods:

  • Utilizing recursion relations to model stress redistribution and fiber survival.
  • Exact calculation of critical stress values for three distinct fiber strength distributions.
  • Derivation of expressions for order parameter, susceptibility, and relaxation dynamics.

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Main Results:

  • An irreversible second-order phase transition from partial to total failure was identified.
  • Exact critical stress values were determined for the studied models.
  • Static and dynamic critical exponents were calculated and found to be universal.

Conclusions:

  • The fiber bundle model exhibits universal critical behavior at the phase transition.
  • The findings provide insights into the failure mechanisms of heterogeneous materials.