Attia Batool

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.

We investigate the failure process of fiber bundles with structural disorder represented by the random misalignment of fibers. The strength of fibers is assumed to be constant so that misalignment is the only source of disorder, which results in a heterogeneous load distribution over fibers. We show by analytical calculations and computer simulations that increasing the amount of structural disorder a transition occurs from a perfectly brittle behavior with abrupt global failure to a quasibrittle phase where failure is preceded by breaking avalanches. The size distribution of avalanches follows a power-law functional form with a complex dependence of the exponent on the amount of disorder. In the vicinity of the critical point the avalanche exponent is 3/2; however, with increasing disorder a crossover emerges to a higher exponent 5/2. We show analytically that the mechanical behavior of the bundle of misaligned fiber with no strength disorder can be mapped to an equal load sharing fiber bundle of perfectly aligned fibers with properly selected strength disorder. Published by the American Physical Society 2024

We investigate how the interplay of the topology of the network of load transmitting connections and the amount of disorder of the strength of the connected elements determines the temporal evolution of failure cascades driven by the redistribution of load following local failure events. We use the fiber bundle model of materials’ breakdown assigning fibers to the sites of a square lattice, which is then randomly rewired using the Watts–Strogatz technique. Gradually increasing the rewiring probability, we demonstrate that the bundle undergoes a transition from the localized to the mean field universality class of breakdown phenomena. Computer simulations revealed that both the size and the duration of failure cascades are power law distributed on all network topologies with a crossover between two regimes of different exponents. The temporal evolution of cascades is described by a parabolic profile with a right handed asymmetry, which implies that cascades start slowly, then accelerate, and eventually stop suddenly. The degree of asymmetry proved to be characteristic of the network topology gradually decreasing with increasing rewiring probability. Reducing the variance of fibers’ strength, the exponents of the size and the duration distribution of cascades increase in the localized regime of the failure process, while the localized to mean field transition becomes more abrupt. The consistency of the results is supported by a scaling analysis relating the characteristic exponents of the statistics and dynamics of cascades.

We investigate the impact-induced damage and fracture of a bar-shaped specimen of heterogeneous materials focusing on how the system approaches perforation as the impact energy is gradually increased. A simple model is constructed which represents the bar as two rigid blocks coupled by a breakable interface with disordered local strength. The bar is clamped at the two ends, and the fracture process is initiated by an impactor hitting the bar in the middle. Our calculations revealed that depending on the imparted energy, the system has two phases: at low impact energies the bar suffers damage but keeps its integrity, while at sufficiently high energies, complete perforation occurs. We demonstrate that the transition from damage to perforation occurs analogous to continuous phase transitions. Approaching the critical point from below, the intact fraction of the interface goes to zero, while the deformation rate of the bar diverges according to power laws as function of the distance from the critical energy. As the degree of disorder increases, farther from the transition point the critical exponents agree with their zero disorder counterparts; however, close to the critical point a crossover occurs to a higher exponent.