Random fiber bundle with many discontinuities in the threshold distribution

Brittle to quasibrittle transition in a compound fiber bundle

The brittle to quasibrittle transition has been studied for a compound of two different kinds of fibrous materials, having distinct difference in their breaking strengths under the framework of the fiber bundle model. A random fiber bundle model has been devised with a bimodal distribution of the breaking strengths of the individual fibers. The bimodal distribution is assumed to consist of two symmetrically placed rectangular probability distributions of strengths p and 1-p, each of width d, and separated by a gap 2s. Different properties of the transition have been studied varying these three parameters and using the well-known equal load-sharing dynamics. Our study exhibits a brittle to quasibrittle transition at the critical width d_{c}(s,p)=p(1/2-s)/(1+p) confirmed by our numerical results.

Stochastic mechanical degradation of multi-cracked fiber bundles with elastic and viscous interactions

The mechanics of fiber bundles has been largely investigated in order to understand their complex failure modes. Under a mechanical load, the fibers fail progressively while the load is redistributed among the unbroken fibers. The classical fiber bundle model captures the most important features of this rupture process. On the other hand, the homogenization techniques are able to evaluate the stiffness degradation of bulk solids with a given population of cracks. However, these approaches are inadequate to determine the effective response of a degraded bundle where breaks are induced by non-mechanical actions. Here, we propose a method to analyze the behavior of a fiber bundle, undergoing a random distribution of breaks, by considering the intrinsic response of the fibers and the visco-elastic interactions among them. We obtain analytical solutions for simple configurations, while the most general cases are studied by Monte Carlo simulations. We find that the degradation of the effective bundle stiffness can be described by two scaling regimes: a first exponential regime for a low density of breaks, followed by a power-law regime at increasingly higher break density. For both regimes, we find analytical effective expressions described by specific scaling exponents.

Avalanche process of the fiber-bundle model with stick-slip dynamics and a variable Young modulus

In order to more accurately describe the fracture process of extensive biological fibers, a fiber-bundle model with stick-slip dynamics and a variable Young modulus is constructed. In this model, the Young modulus of a fiber is assumed to increase or decrease by multiplying with a changing ratio after local sliding events. So, the maximum number of stick-slip events of a single fiber and the changing ratio of the Young modulus are the two key parameters of the model. By means of analytical theory and numerical simulation, the constitutive law, the critical stress, the average size of the largest avalanche, and the avalanche size distribution are shown against the two parameters of the model. From a macroscopic viewpoint, the constitutive curves show different morphologies varying from a local plastic state to a unimodal parabola, while from a microscopic viewpoint, the avalanche size distributions can be well fitted into a power law relationship, which is in accord with the classical fiber-bundle model.