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Simulation of finite size effects of the fiber bundle model

Author

Listed:
  • Hao, Da-Peng
  • Tang, Gang
  • Xun, Zhi-Peng
  • Xia, Hui
  • Han, Kui

Abstract

In theory, the macroscopic fracture of materials should correspond with the thermodynamic limit of the fiber bundle model. However, the simulation of a fiber bundle model with an infinite size is unrealistic. To study the finite size effects of the fiber bundle model, fiber bundle models of various size are simulated in detail. The effects of system size on the constitutive behavior, critical stress, maximum avalanche size, avalanche size distribution, and increased step number of external load are explored. The simulation results imply that there is no feature size or cut size for macroscopic mechanical and statistical properties of the model. The constitutive curves near the macroscopic failure for various system size can collapse well with a simple scaling relationship. Simultaneously, the introduction of a simple extrapolation method facilitates the acquisition of more accurate simulation results in a large-limit system, which is better for comparison with theoretical results.

Suggested Citation

  • Hao, Da-Peng & Tang, Gang & Xun, Zhi-Peng & Xia, Hui & Han, Kui, 2018. "Simulation of finite size effects of the fiber bundle model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 338-346.
    • Handle: RePEc:eee:phsmap:v:490:y:2018:i:c:p:338-346
    DOI: 10.1016/j.physa.2017.08.087
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    References listed on IDEAS

    as
    1. Hao, Da-Peng & Tang, Gang & Xun, Zhi-Peng & Xia, Hui & Han, Kui, 2016. "Simulation study on the avalanche process of the mixed brittle–plastic fiber bundle model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 441(C), pages 237-244.
    2. Dill-Langer, G & Hidalgo, R.Cruz & Kun, F & Moreno, Y & Aicher, S & Herrmann, H.J, 2003. "Size dependency of tension strength in natural fiber composites," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 325(3), pages 547-560.
    3. Aarão Reis, F.D.A., 2006. "Roughness fluctuations, roughness exponents and the universality class of ballistic deposition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 190-196.
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    Cited by:

    1. Hao, Da-Peng & Tang, Gang & Xun, Zhi-Peng & Xia, Hui & Han, Kui, 2018. "The avalanche process of the fiber bundle model with defect in local loading sharing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 1095-1102.

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