The Fiber Bundle

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Background

The basic concept of the fiber bundle model was introduced almost a hundred years ago by Peirce to understand the strength of cotton yarns. Early developments of the model continued along this line, focusing on bundles of threads of random strength incorporating time-dependent deformation as well as damaging. Already this basic setup of the model provided a surprisingly deep insight into the microscopic dynamics of the failure of fibrous materials. Subsequently, these early works initiated an intense research in both the engineering and physics communities, making the fiber bundle model not only an alternative to continuum approaches but an essential model for the understanding of the damage and fracture of a broad class of materials.

Disorder is an inherent property of natural and of most artificially made materials, which plays a crucial role in fracture. Most notably, on the micro-scale, the fracture of disordered materials proceeds in intermittent bursts characterized by scale-free statistics, while the front of propagating cracks and the surface left behind exhibit a high degree of roughness. On the macro-scale, the ultimate strength of disordered materials shows a strong statistical variation with an average depending on the sample size. Such findings showed that a comprehensive understanding of the fracture of disordered materials can only be achieved in the framework of statistical physics. During the last three decades the fiber bundle model became a generic modelling framework of the statistical physics of fracture and provided essential contributions, for instance, to reveal emerging universal features of fracture, to clarify its analogy to phase transitions and critical phenomena, and to unveil relations of observables that can be exploited to forecast the imminent catastrophic failure.

Recent applications of the fiber bundle model have covered a fascinating diversity of systems such as the failure of compressed nano-pillars, rupture of collagen fibers in cells, statistics of force chains in granular materials, enhanced stability of soils due to reinforcement by plant roots, initiation of snow avalanches and landslides in mountains, development of failure forecast methods for fracture and earthquakes. Even in the broader context of complex systems and non-equilibrium phase transitions, the fiber bundle model has proven successful, providing an excellent testing ground of ideas.

This Research Topic focuses on the theoretical and methodological developments, as well as on the cross-disciplinary applications of the fiber bundle modelling approach. We call for contributions to discuss the present status and promising future directions where the fiber bundle model may play a relevant role.

The Research Topic is intended to cover subjects such as:
- Statistical physics of fracture and breakdown phenomena
- Fracture-failure as a critical phenomenon
- Statistics and dynamics of avalanches
- Time dependent fracture (fatigue and creep)
- Fracture propagation in disordered media
- Design of novel materials (hierarchically structured and metamaterials, etc.)
- Failure forecast methods
- Application of FBM in modelling rock-fracturing, landslides, snow avalanches, etc.

Keywords: Fiber bundle model, Damage, Fracture, Statistical physics, Materials science

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