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