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We study a model of ``organized'' criticality, where a single avalanche propagates through an \textit{a priori} static (i.e., organized) sandpile configuration. The latter is chosen according to an i.i.d. distribution from a Borel…
We investigate compressive failure of heterogeneous materials on the basis of a continuous progressive damage model. The model explicitely accounts for tensile and shear local damage and reproduces the main features of compressive failure…
Cavitation has long been recognized as a crucial predictor, or precursor, to the ultimate failure of various materials, ranging from ductile metals to soft and biological materials. Traditionally, cavitation in solids is defined as an…
The mechanical behavior of porous materials depends strongly on porosity and pore geometry, but also on morphological parameters characterizing the spatial arrangement of pores. Here we use bond-based peridynamics to study effects of…
We carried out a finite-size scaling analysis of the restricted solid-on-solid version of a recently introduced growth model that exhibits a roughening transition accompanied by spontaneous symmetry breaking. The dynamic critical exponent…
We introduce a model for yielding, inspired by fracture models and the failure of a sheared granular medium in which the applied shear is resisted by self-organized force chains. The force chains in the granular medium (GM) are considered…
In the context of Monte Carlo simulations, the analysis of the probability distribution $P_L(m)$ of the order parameter $m$, as obtained in simulation boxes of finite linear extension $L$, allows for an easy estimation of the location of…
We investigate numerically and theoretically the precursory intermittent activity characterizing the preliminary phase of damage accumulation prior to failure of quasi-brittle solids. We use a minimal but thermodynamically consistent model…
We discuss the Euclidean quantum $O(N)$ model with $N=2$ in a continuous broken symmetry phase. We study the system at low temperatures in the presence of quenched disorder linearly coupled to the scalar field. Performing an average over…
The fact that a disordered material is not constrained in its properties in the same way as a crystal presents significant and yet largely untapped potential for novel material design. However, unlike their crystalline counterparts,…
This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary…
We study the creep rupture of fiber composites in the framework of fiber bundle models. Two novel fiber bundle models are introduced based on different microscopic mechanisms responsible for the macroscopic creep behavior. Analytical and…
We study the approach to global breakdown in disordered media driven by increasing external forces. We first analyze the problem by mean-field theory, showing that the failure process can be described as a first-order phase transition,…
Studies of nucleation generally focus on the properties of the critical cluster, but the presence of defects within the crystal lattice means that the population of nuclei necessarily evolve through a distribution of pre-critical clusters…
We study the subsampling of the avalanches in the fiber bundle model of fracture. In cases where only a part of the system is observed for the micro-failure events, the recorded avalanche statistics gets distorted compared to the actual…
We consider a correlated site percolation problem on a cubic lattice of size $L^3$, with $16\le L\le 512$. The sites of an initially full lattice are removed by a random walk of ${\cal N}=uL^3$ steps. When the parameter $u$ crosses a…
A prototype statistical model for the etching of a random solid is investigated in order to assess the influence of disorder and temperature on the dissolution kinetics. At low temperature, the kinetics is dominated by percolation…
Neural avalanches are collective firings of neurons that exhibit emergent scale-free behavior. Understanding the nature and distribution of these avalanches is an important element in understanding how the brain functions. We study a model…
The statistical properties of failure are studied in a fiber bundle model with thermal noise. We find that in agreement with recent experiments the macroscopic failure is produced by a thermal activation of microcracks. Most importantly the…
The critical behaviour of a Random Fiber Bundle Model with mixed uniform distribution of threshold strengths and global load sharing rule is studied with a special emphasis on the nature of distribution of avalanches for different…