Related papers: Introduction to Critical Phenomena through the Fib…
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…
The dynamics of a fibre-bundle type model with equal load sharing rule is numerically studied. The system, formed by N elements, is driven by a slow increase of the load upon it which is removed in a novel way through internal transfers to…
This chapter introduces the fracture nucleation process, their (extreme) statistics in disordered solids, in fiber bundle models, and in the two fractal overlap models of earthquake.
Disorder and long-range interactions are two of the key components that make material failure an interesting playfield for the application of statistical mechanics. The cornerstone in this respect has been lattice models of the fracture in…
We investigate the fracture of heterogeneous materials occurring under unloading from an initial load. Based on a fiber bundle model of time dependent fracture, we show that depending on the unloading rate the system has two phases: for…
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…
We study the phase transition in a class of fiber bundle models in which the fiber strengths are distributed randomly within a finite interval and global load sharing is assumed. The dynamics is expressed as recursion relations for the…
Various kinds of heterogeneity in solids including atomistic discreteness affect the fracture strength as well as the failure dynamics remarkably. Here we study the effects of an initial crack in a discrete model for fracture in…
In this paper a composite model for earthquake rupture initiation and propagation is proposed. The model includes aspects of damage mechanics, fiber-bundle models, and slider-block models. An array of elements is introduced in analogy to…
The statistical properties of failure are studied in a fiber bundle model with thermal noise. We show that the macroscopic failure is produced by a thermal activation of microcracks. Most importantly the effective temperature of the system…
Fracture processes in heterogeneous materials comprise a large number of disordered spatial degrees of freedom, representing the dynamical state of a sample over the entire domain of interest. This complexity is usually modeled directly,…
In the present paper, a fiber bundle model in (1+1)-dimensions that simulates the rupture process of a fibrous material pulled by an uniaxial force F is analyzed. In this model the load of a broken fiber is shifted in equal portions onto…
We study the existence of distinct failure regimes in a model for fracture in fibrous materials. We simulate a bundle of parallel fibers under uniaxial static load and observe two different failure regimes: a catastrophic and a slowly…
The study reports a systematic evaluation of the role of spatially correlated mechanical elements on failure behavior of heterogeneous materials represented by fiber bundle models (FBM) with different load redistribution rules. The increase…
Fiber bundle models (FBM's) have been used to model the failure of fibrous composites as load-sharing systems since the 1960's when Rosen (1964 and 1965) conducted some remarkable experiments on unidirectional fibrous composites. These…
In this work we review the precursors of catastrophic avalanches (global failures) in several failure models, namely (a) Fiber Bundle Model (FBM), (b) Random Fuse Model (RFM), (c) Sandpile Models and (d) Fractal Overlap Model. The precursor…
Using the global fiber bundle model as a tractable scheme of progressive fracture in heterogeneous materials, we define the branching ratio in avalanches as a suitable order parameter to clarify the order of the phase transition occurring…
We study random fiber bundle model (RFBM) with different threshold strength distributions and load sharing rules. A mixed RFBM within global load sharing scheme is introduced which consists of weak and strong fibers with uniform…
We study the constitutive behaviour, the damage process, and the properties of bursts in the continuous damage fiber bundle model introduced recently. Depending on its two parameters, the model provides various types of constitutive…
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…