Continuous Damage Fiber Bundle Model for Strongly Disordered Materials

TL;DR

This paper introduces an extended fiber bundle model that captures the gradual failure and crack propagation in highly heterogeneous materials, emphasizing the role of disorder and extreme value statistics in failure dynamics.

Contribution

It develops a novel continuous damage fiber bundle model incorporating random degradation steps and failure thresholds, advancing understanding of failure in disordered materials.

Findings

Failure process governed by extreme value statistics

Disorder significantly influences macroscopic behavior

Microscopic bursting activity affected by failure thresholds

Abstract

We present an extension of the continuous damage fiber bundle model to describe the gradual degradation of highly heterogeneous materials under an increasing external load. Breaking of a fiber in the model is preceded by a sequence of partial failure events occurring at random threshold values. In order to capture the subsequent propagation and arrest of cracks, furthermore, the disorder of the number of degradation steps of material constituents, the failure thresholds of single fibers are sorted into ascending order and their total number is a Poissonian distributed random variable over the fibers. Analytical and numerical calculations showed that the failure process of the system is governed by extreme value statistics, which has a substantial effect on the macroscopic constitutive behaviour and on the microscopic bursting activity as well.