A computationally-efficient hierarchical scaling law to predict damage accumulation in composite fibre-bundles

Unidirectional composites under longitudinal tension develop damage through the accumulation and clustering of fibre-breaks, which may lead to catastrophic failure of an entire structure. This paper uses a hierarchical scaling law to predict the kinetics of fibre-breakage and its effect on the stress-strain response of composites under longitudinal tension; due to its analytical formulation based on the statistical analysis of hierarchical fibre-bundles, the scaling law predicts the response of composite bundles up to virtually any size in less than one second. Model predictions for the accumulation and clustering of fibre-breaks are successfully validated against experiments from the literature. These results show that the present model is a much more computationally-efficient alternative to other state-of-the-art models based on Monte-Carlo simulations, without sacrificing the accuracy of predictions when compared against experiments.