Abstract
We observe the failure process of a fiber bundle model with a variable stress release range, γ, and higher the value of γ, lower the stress release range. By tuning γ from low to high, it is possible to go from the mean-field (MF) limit of the model to the local load-sharing (LLS) limit where local stress concentration plays a crucial role. In the MF limit, individual avalanches (number of fibers breaking in going from one stable state to the next, s) and the corresponding energies E emitted during those avalanches have one-to-one linear correlation. This results in the same size distributions for both avalanches (P(s)) and energy bursts (Q(E)): a scale-free distribution with a universal exponent value of −5/2. With increasing γ, the model enters the LLS limit beyond some γc. In this limit, due to the presence of local stress concentrations around a damaged region, such correlation C(γ) between s and E decreases, i.e., a smaller avalanche can emit a large amount of energy or a large avalanche may emit a small amount of energy. The nature of the decrease in the correlation between s and E depends highly on the dimension of the bundle. In this work, we study the decrease in the correlation between avalanche size and the corresponding energy bursts with an increase in the load redistribution localization in the fiber bundle model in one and two dimensions. Additionally, we note that the energy size distribution remains scale-free for all values of γ, whereas the avalanche size distribution becomes exponential for γ > γc.
Highlights
Disordered materials, when subjected to external stress, go through local damages that eventually emerge as a catastrophic fracture when the load exceeds a critical value
While the average values of energy bursts (〈E〉) and avalanche sizes or damage (〈s〉) are known in those systems, in this work, we focus on how does the individual correspondence between the avalanche size and energy of a particular event vary with localization of load redistribution in the context of the fiber bundle model in one and two dimensions
The distribution of avalanches and emitted energies are shown, and a connection between them is established through the correlation function
Summary
Disordered materials, when subjected to external stress, go through local damages that eventually emerge as a catastrophic fracture when the load exceeds a critical value. While the average values of energy bursts (〈E〉) and avalanche sizes or damage (〈s〉) are known in those systems, in this work, we focus on how does the individual correspondence between the avalanche size and energy of a particular event vary with localization of load redistribution in the context of the fiber bundle model in one and two dimensions. It was noted earlier [13] that in the extreme limit of the nearest neighbor load sharing, those avalanches of large sizes can have small energy release and vice versa. The nature of decreases and the size distribution of the two quantities depend strongly on the dimensionality of the model
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