Related papers: Exact numerical solution for a time-dependent fibe…
A time-dependent global fiber-bundle model of fracture with continuous damage is formulated in terms of a set of coupled non-linear differential equations. A first integral of this set is analytically obtained. The time evolution of the…
In this work, we present a numerical method that provides accurate real-time detection for the widths of the fractures in a fractured porous medium based on observational data on porous medium fluid mass and velocity. To achieve this task,…
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 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…
In this paper, numerical analysis is carried out for a class of history-dependent variational-hemivariational inequalities arising in contact problems. Three different numerical treatments for temporal discretization are proposed to…
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…
Strengthening of materials and preventing abrupt fracture are really challenging jobs in the field of engineering and material science. Such problems can be resolved by using composite materials. In this work, we have studied the fracture…
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 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 propose and analyze an adaptive finite element method for a phase-field model of dynamic brittle fracture. The model couples a second-order hyperbolic equation for elastodynamics with the Ambrosio-Tortorelli regularization of the…
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…
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…
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…
In this work we present the mathematical models for single-phase flow in fractured porous media. An overview of the most common approaches is considered, which includes continuous fracture models and discrete fracture models. For the…
This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. Moreover, stability and convergence…
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 this paper, we numerically address the inverse problem of identifying a time-dependent coefficient in the time-fractional diffusion equation. An a priori estimate is established to ensure uniqueness and stability of the solution. A fully…
In the paper, we propose a new effective mathematical formulation and resulting universal numerical algorithm capable of tackling various HF models in the framework of a unified approach. The presented numerical scheme is not limited to any…
The average time for the onset of macroscopic fractures is analytically and numerically investigated in the fiber-bundle model with quenched disorder and thermal noise under a constant load. We find an implicit exact expression for the…
In this paper we establish the convergence of a numerical scheme based, on the Finite Element Method, for a time-independent problem modelling the deformation of a linearly elastic elliptic membrane shell subjected to remaining confined in…