Inequality Indices Applied to Statistical Physics of Criticality in an Impregnated Fiber Bundle Model

Inequality indices (Hirsch and Kolkata) are used in social science and scientometrics. Previously, they were shown to have useful applications in statistical physics of criticality in a Fiber Bundle Model (FBM) with an Equal Load Sharing (ELS). The indices offer potentially useful techniques for predicting the imminent failure of the bundle. In this paper, the same indices are calculated for the case of an Impregnated Fiber Bundle Model (IFBM) with physically based load redistributions around fiber breaks based on finite element model stress fields. It is shown that the behavior of the Hirsch and Kolkata indices in this case are similar to the behavior in the FBM with ELS, including similar critical values for the final failure of the bundle.