Avalanche dynamics of the continuous damage fiber bundle model

We present a detailed analytical and numerical study of the avalanche statistics of the continuous damage fiber bundle model. In the model, linearly elastic fibers undergo a series of partial failure events which give rise to a gradual degradation of their stiffness. Varying the two parameters of the model, i.e. the maximum number of local failures and the degree of stiffness reduction in single events, the model provides various types of material responses with experimental relevance. We show by analytic calculations that the presence of plasticity and hardening in the macroscopic constitutive behavior results in power law distributed breaking bursts with a spectrum of exponents. We derive the phase diagram of the model system, which provides an overview of all possible burst distributions. Our results generalize previous analytical findings and bring a new unified view of the statistics of breaking avalanches in fiber bundles models.