Abstract
We discuss the cooperative failure dynamics in the fiber bundle model where the individual elements or fibers are Hookean springs that have identical spring constants but different breaking strengths. When the bundle is stressed or strained, especially in the equal-load-sharing scheme, the load supported by the failed fiber gets shared equally by the rest of the surviving fibers. This mean-field-type statistical feature (absence of fluctuations) in the load-sharing mechanism helped major analytical developments in the study of breaking dynamics in the model and precise comparisons with simulation results. We intend to present a brief review on these developments.
Highlights
Fiber bundle model (FBM) has been used widely for studying the fracture and failure [1] of composite materials under external loading
While the details of the avalanche dynamics seen in the fiber bundle model with quasi-static load increase has been discussed elsewhere in this special issue [32], here we briefly describe the avalanche dynamics for fixed amount load increase, that is, when the system is in a stable condition, a fixed amount of load δ is added, which restarts the dynamics
There are several factors that can help rupture evolution, like friction, plasticity, fluid migration, spatial heterogeneities, chemical reactions, etc. To some extent, such stress redistribution/localization can be taken into account through a proper load sharing scheme and a noise term (T) can in principle represent the combined effect of all other factors
Summary
Fiber bundle model (FBM) has been used widely for studying the fracture and failure [1] of composite materials under external loading. Even though FBM was designed initially as a model for the fracture or failure of a set of parallel elements (fibers), having different breaking thresholds, with a collective load-sharing scheme, the failure dynamics in the model shows all the attributes of the critical phenomena and the associated phase transition. It seems, due to the usefulness and richness, FBM plays the same role (in the field of fracture) as the Ising model in magnetism [22]. We have a short Summary and Conclusion section (Section 6) at the end
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