# Variation of elastic energy shows reliable signal of upcoming catastrophic failure

## TL;DR

This paper demonstrates that the slope of elastic energy versus strain reliably signals imminent catastrophic failure in fiber bundle models, with potential applications in predicting failure in composite materials.

## Contribution

It introduces a novel analytical and numerical analysis of elastic energy behavior as a precursor to failure in fiber bundle models, highlighting the slope maximum as a predictive indicator.

## Key findings

- Elastic energy peaks after failure, but its slope peaks beforehand.
- The slope maximum reliably predicts upcoming catastrophic failure.
- Results are validated for power-law and Weibull fiber threshold distributions.

## Abstract

We consider the Equal-Load-Sharing Fiber Bundle Model as a model for composite materials under stress and derive elastic energy and damage energy as a function of strain. With gradual increase of stress (or strain) the bundle approaches a catastrophic failure point where the elastic energy is always larger than the damage energy. We observe that elastic energy has a maximum that appears after the catastrophic failure point is passed, i.e., in the unstable phase of the system. However, the slope of elastic energy vs. strain curve has a maximum which always appears before the catastrophic failure point and therefore this can be used as a reliable signal of upcoming catastrophic failure. We study this behavior analytically for power-law type and Weibull type distributions of fiber thresholds and compare the results with numerical simulations on a single bundle with large number of fibers.