Related papers: Time dependence of breakdown in a global fiber-bun…
A time-dependent global fiber-bundle model of fracture with continuous damage was recently formulated in terms of an autonomous differential system and numerically solved by applying a discrete probabilistic method. In this paper we provide…
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…
We present an extension of the continuous damage fiber bundle model to describe the gradual degradation of highly heterogeneous materials under an increasing external load. Breaking of a fiber in the model is preceded by a sequence of…
We study the time evolution of damage in a fiber bundle model in which the range of interaction of fibers varies through an adjustable stress transfer function recently introduced. We find that the lifetime of the material exhibits a…
A probabilistic method for solving time-dependent load-transfer models of fracture is developed. It is applicable to any rule of load redistribution, i.e, local, hierarchical, etc. In the new method, the fluctuations are generated during…
We present a general prediction scheme of failure times based on updating continuously with time the probability for failure of the global system, conditioned on the information revealed on the pre-existing idiosyncratic realization of the…
We introduce a continuous damage fiber bundle model that gives rise to macroscopic plasticity and compare its behavior with that of dry fiber bundles. Several interesting constitutive behaviors are found in this model depending on the value…
We study fracture processes within a stochastic fiber-bundle model where it is assumed that after the failure of a fiber, each intact fiber obtains a random fraction of the failing load. Within a Markov approximation, the breakdown…
A realistic continuous-time dynamics for fiber bundles is introduced and studied both analytically and numerically. The equation of motion reproduces known stationary-state results in the deterministic limit while the system under…
A fiber bundle model in $(1+1)$-dimensions for the breaking of fibrous composite matrix is introduced. The model consists of $N$ parallel fibers fixed in two plates. When one of the plates is pulled in the direction parallel to the fibers,…
We study the scaling behaviors of a time-dependent fiber-bundle model with local load sharing. Upon approaching the complete failure of the bundle, the breaking rate of fibers diverges according to $r(t)\propto (T_f-t)^{-\xi}$, where $T_f$…
The study of temporal networks in discrete time has yielded numerous insights into time-dependent networked systems in a wide variety of applications. For many complex systems, however, it is useful to develop continuous-time models of…
Prediction of breakdown in disordered solids under external loading in a question of paramount importance. Here we use a fiber bundle model for disordered solids and record the time series of the avalanche sizes and energy bursts. The time…
The possible paralelism existing between phase transitions and fracture in disordered materials, is discussed using the well-known Fiber Bundle Models and a probabilistic approach suited to smooth fluctuations near the critical point. Two…
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…
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,…
Statistical models are essential to get a better understanding of the role of disorder in brittle disordered solids. Fiber bundle models play a special role as a paradigm, with a very good balance of simplicity and non-trivial effects. We…
The fiber bundle model describes a collection of elastic fibers under load. the fibers fail successively and for each failure, the load distribution among the surviving fibers change. Even though very simple, the model captures the…
We introduce a fiber bundle model where the interaction among fibers is modeled by an adjustable stress-transfer function which can interpolate between the two limiting cases of load redistribution, the global and the local load sharing…
We discuss the identification of a time-dependent potential in a time-fractional diffusion model from a boundary measurement taken at a single point. Theoretically, we establish a conditional Lipschitz stability for this inverse problem.…