Time dependence of breakdown in a global fiber-bundle model with continuous damage

Continuous damage fiber bundle model for strongly disordered materials

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. The breaking of a fiber in the model is preceded by a sequence of partial failure events occurring at random threshold values. In order to capture the subsequent propagation and arrest of cracks, furthermore, the disorder of the number of degradation steps of material constituents, the failure thresholds of single fibers, are sorted into ascending order and their total number is a Poissonian distributed random variable over the fibers. Analytical and numerical calculations showed that the failure process of the system is governed by extreme value statistics, which has a substantial effect on the macroscopic constitutive behavior and on the microscopic bursting activity as well.

Load capacity and rupture displacement in viscoelastic fiber bundles

We study the creep rupture of viscoelastic fiber bundles under uniaxial constant tensile loading, assuming global load sharing (GLS) for the redistribution of load following fiber failure. We consider loading paths such that the stress raises to a value sigma0 under a time-independent loading (negligible creep strain) and remains fixed thereafter. Motivated by experimental observations, we introduce an "effective" strain controlled failure criterion to incorporate damage into the system, thus damage is distributed over time. In addition, when a "limit" value for the effective stress is reached, failure of the remaining alive fibers is instantaneous. This enables us to show both analytically and numerically that creep rupture occurs for external loads above a critical value that is less than the static fracture bundle's strength in accordance with experimental observations. An analytical expression for this critical load is given. For stress levels below the critical value, the system suffers only partial failure since the deformation tends to a stationary solution for which the effective stress is below the limit value giving rise to an infinite lifetime. On the other hand, if the time-independent loading process ends in the softening regime, the deformation of the system monotonically increases in time resulting in global failure at finite time irrespectively of the applied load. Moreover, the applied model is found to be consistent with the experimentally observed increase of the creep rupture displacement with decreasing steady external load (above the critical value).

Health status and resonance in a model for living organisms under periodic stress and healing

We apply the dynamic model for failures to a living organism under periodic stress and study how the health status of the organism evolves. It is found that without healing, the average fraction of intact cells decays either stepwise to zero or to a constant value far from zero, depending on the peak value of the periodic stress. As the parameter measuring the healing probability is raised from zero, the fraction exhibits oscillating behavior, reminiscent of periodic synchronization. The power spectrum at the stress frequency at first increases with the healing parameter, then decreases, which may be called healing resonance. We also study the time evolution of the system in the case that the healing parameter varies periodically with time and observe a transition from the unhealthy state to the healthy one as the healing frequency increases. This suggests how to adjust the frequency of medical treatment to the optimum.

Time evolution of damage under variable ranges of load transfer

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 crossover from mean-field to short-range behavior as in the static case. Numerical calculations showed that the value at which the transition takes place depends on the system's disorder. Finally, we have performed a microscopic analysis of the failure process. Our results confirm that the growth dynamics of the largest crack is radically different in the two limiting regimes of load transfer during the first stages of breaking.

Scaling laws of creep rupture of fiber bundles

We study the creep rupture of fiber composites in the framework of fiber bundle models. Two fiber bundle models are introduced based on different microscopic mechanisms responsible for the macroscopic creep behavior. Analytical and numerical calculations show that above a critical load the deformation of the creeping system monotonically increases in time resulting in global failure at a finite time t(f), while below the critical load the system suffers only partial failure and the deformation tends to a constant value giving rise to an infinite lifetime. It is found that approaching the critical load from below and above the creeping system is characterized by universal power laws when the fibers have long-range interaction. The lifetime of the composite above the critical point has a universal dependence on the system size.

Phase transition in fiber bundle models with recursive dynamics

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 redistribution of the applied stress and the evolution of the surviving fraction of fibers. We show that an irreversible phase transition of second-order occurs, from a phase of partial failure to a phase of total failure, when the initial applied stress just exceeds a critical value. The phase transition is characterized by static and dynamic critical properties. We calculate exactly the critical value of the initial stress for three models of this kind, each with a different distribution of fiber strengths. We derive exact expressions for the order parameter, the susceptibility to changes in the initial applied stress, and the critical relaxation of the surviving fraction of fibers for all the three models. The static and dynamic critical exponents obtained from these expressions are found to be universal.

Bursts in a fiber bundle model with continuous damage

We study the constitutive behavior, 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 behaviors including macroscopic plasticity. Analytical results are obtained to characterize the damage process along the plastic plateau under strain controlled loading; furthermore, for stress controlled experiments we develop a simulation technique, and numerically explore the distribution of bursts of fiber breaks assuming an infinite range of interaction. Simulations revealed that under certain conditions power law distribution of bursts arises with an exponent significantly different from the mean field exponent 5/2. A phase diagram of the model characterizing the possible burst distributions is constructed.