Effect of the range of interaction on the time evolution of failure cascades

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Abstract
We investigate how the range of interaction between system elements influences the statistical and temporal characteristics of failure cascades in driven disordered systems. Focusing on creep-induced failure of heterogeneous materials under constant external load, we employ a fibre bundle model in which elements of random strength are arranged on a square lattice and the load released by failed fibres is redistributed according to a distance-dependent power law. This formulation allows the effective interaction range to be tuned continuously between equal-load-sharing and localized-load-sharing limits. We show that both avalanche size and duration distributions exhibit power-law behaviour, with exponents that vary systematically with the interaction range, signalling a broad crossover from mean-field-like global load sharing to stress-concentration-dominated localized load sharing. Beyond avalanche statistics, we analyse the temporal evolution of individual events and demonstrate that their average activity profiles are generically parabolic. Crucially, the symmetry of these profiles is highly sensitive to the interaction range: long-range redistribution produces symmetric, mean-field-like avalanches, whereas localized interactions lead to strongly right-skewed profiles. These results provide a unified statistical and dynamical characterization of failure cascades and highlight avalanche profile asymmetry as a robust indicator of interaction range, with potential applications in non-destructive evaluation based on acoustic emission signals.
Funding Information
  • University of Debrecen Program for Scientific Publication
  • National Research, Development and Innovation Fund of Hungary (TKP2021-NKTA)

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