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The random fiber bundle (RFB) model, with the strength of the fibers distributed uniformly within a finite interval, is studied under the assumption of global load sharing among all unbroken fibers of the bundle. At any fixed value of the…
The collective strength of a system of fibers, each having a failure threshold drawn randomly from a distribution, indicates the maximum load carrying capacity of different disordered systems ranging from disordered solids, power-grid…
The effect of quenched disorder on non-equilibrium phase transitions in the directed percolation universality class is studied by a strong disorder renormalization group approach and by density matrix renormalization group calculations. We…
We study size effects in the fracture strength of notched disordered samples using numerical simulations of lattice models for fracture. In particular, we consider the random fuse model, the random spring model and the random beam model,…
The topology of the network of load transmitting connections plays an essential role in the cascading failure dynamics of complex systems driven by the redistribution of load after local breakdown events. In particular, as the network…
The collapse of weakly turbulent prestellar cores is a critical stage in the process of star formation. Being highly non-linear and stochastic, the outcome of collapse can only be explored theoretically by performing large ensembles of…
We analyze the failure process of a two-component system with widely different fracture strength in the framework of a fiber bundle model with localized load sharing. A fraction 0\leq \alpha \leq 1 of the bundle is strong and it is…
In this paper I have studied the fiber bundle model with a fraction {\alpha} of infinitely strong fibers. Inclusion of such unbreakable fraction has been proven to affect the failure process in early studies, especially around a critical…
We consider the effect of nucleation on a one-dimensional stepped surface, finding that step-flow growth is metastable for any strength of the additional step-edge barrier. The surface is made unstable by the formation of a critical…
The statistics of burst avalanche sizes $n$ during failure processes in a fiber bundle follows a power law, $D(n)\sim n^{-\xi}$, for large avalanches. The exponent $\xi$ depends upon how the avalanches are provoked. While it is known that…
Continuum mechanics describes compressive failure as a standard bifurcation in the response of a material to an increasing load: damage, which initially grows uniformly in the material, localizes within a thin band at failure. Yet,…
Our goal is to unravel the mechanisms that lead to failure of a ductile two-phase material - that consists of a ductile soft phase and a relatively brittle hard phase. An idealized microstructural model is used to study damage propagation…
The primary factors controlling defect stability in phase-field crystal (PFC) models are examined, with illustrative examples involving several existing variations of the model. Guidelines are presented for constructing models with stable…
We study slip avalanches in disordered materials under an increasing external load in the framework of a fiber bundle model. Over-stressed fibers of the model do not break, instead they relax in a stick-slip event which may trigger an…
The yield behavior of crystalline solids is determined by the motion of defects like dislocations, twin boundaries and coherent phase boundaries. These solids are hardened by introducing precipitates -- small particles of a second phase. It…
We show that disordered boundaries destroy bulk phase separation in scalar active systems in dimension $d<d_c=3$. This is in strong contrast with the equilibrium case where boundaries have no impact on the bulk of phase-separated systems.…
In biological materials, strong binding despite an applied load force is often based on clusters of dynamic bonds that share the load. Different macroscopic behaviors have been described depending on whether the load is shared locally or…
Contacts at the Coulomb threshold are unstable to tangential perturbations and thus contribute to failure at the microscopic level. How is such a local property related to global failure, beyond the effective picture given by a Mohr-Coulomb…
We investigate the approach to catastrophic failure in a model porous granular material undergoing uniaxial compression. A discrete element computational model is used to simulate both the micro-structure of the material and the complex…
A bundle of fibers has been considered here as a model for composite materials, where breaking of the fibers occur due to a combined influence of applied load (stress) and external noise. Through numerical simulation and a mean-field…