Ferenc Kun

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 shrinkage induced breakup of thin layers of heterogeneous materials attached to a substrate, a ubiquitous natural phenomenon with a wide range of potential applications. Focusing on the evolution of the fragment ensemble, we demonstrate that the system has two distinct phases: damage phase, where the layer is cracked, however, a dominant piece persists retaining the structural integrity of the layer, and a fragmentation phase, where the layer disintegrates into numerous small pieces. Based on finite size scaling we show that the transition between the two phases occurs at a critical damage analogous to continuous phase transitions. At the critical point a fully connected crack network emerges whose structure is controlled by the strength of adhesion to the substrate. In the strong adhesion limit, damage arises from random microcrack nucleation, resembling bond percolation, while weak adhesion facilitates stress concentration and the growth of cracks to large extensions. The critical exponents of the damage to fragmentation transition agree to a reasonable accuracy with those of two-dimensional bond percolation. Our findings provide a novel insights into the mechanism of shrinkage-induced cracking revealing generic scaling laws of the phenomenon.

We investigate the fragmentation of ring-like brittle structures under explosive loading using a discrete element model. By systematically varying ring thickness and strain rate, we uncover a transition from one-dimensional (1D) segmentation to two-dimensional (2D) planar fragmentation and, ultimately, to complete shattering. This transition is driven by the effective dimensionality of the crack pattern, which evolves with increasing strain rate. We identify a critical ring thickness beyond which segmentation ceases, and fragmentation directly follows a power-law mass distribution characteristic of 2D systems. In the crossover regime, spanning and non-spanning fragments coexist, enabling control over the power-law exponent of the mass distribution. At very high strain rates, we observe a transition to complete shattering, where the system follows a novel scaling law relating the shattering strain rate to ring thickness. Our results provide fundamental insights into fragmentation universality classes and offer potential applications in space debris prediction, controlled detonation technologies, and materials engineering.

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

Based on computer simulations of a realistic discrete element model we demonstrate that shrinkage induced cracking of thin layers of heterogeneous materials, generating spectacular crack patterns, proceeds in bursts. These crackling pulses are characterized by scale free distributions of size and duration, however, with non-universal exponents depending on the system size and shrinking rate. On the contrary, local avalanches composed of micro-cracking events with temporal and spatial correlation are found to obey a universal power law statistics. Most notably, we demonstrate that the observed non-universality of the integrated signal is the consequence of the temporal superposition of the underlying local avalanches, which pop up in an uncorrelated way in homogeneous systems. Our results provide an explanation of recent acoustic emission measurements on drying induced shrinkage cracking and may have relevance for the acoustic monitoring of the electro-mechanical degradation of battery electrodes.