# Creep failure of hierarchical materials

## TL;DR

This paper studies how hierarchical structures in materials affect their long-term strength and failure under constant stress.

## Contribution

The study introduces a new failure mode in hierarchical materials that differs from traditional crack-based failure.

## Key findings

- Hierarchical patterning increases creep strain and lifetime while reducing variation.
- The new failure mode aligns with experimental results on patterned paper sheets.
- Hierarchical structures induce different failure mechanisms compared to random cross-linking.

## Abstract

Creep failure of hierarchical materials is investigated by simulation of beam network models. Such models are idealizations of hierarchical fibrous materials where bundles of load-carrying fibers are held together by multi-level (hierarchical) cross-links. Failure of individual beams is assumed to be governed by stress-assisted thermal activation over local barriers, and beam stresses are computed by solving the global balance equations of linear and angular momentum across the network. Disorder is mimicked by a statistical distribution of barrier heights. Both initially intact samples and samples containing side notches of various length are considered. Samples with hierarchical cross-link patterns are simulated alongside reference samples where cross-links are placed randomly without hierarchical organization. The results demonstrate that hierarchical patterning may strongly increase creep strain and creep lifetime while reducing the lifetime variation. This is due to the fact that hierarchical patterning induces a failure mode that differs significantly from the standard scenario of failure by nucleation and growth of a critical crack. Characterization of this failure mode demonstrates good agreement between the present simulations and experimental findings on hierarchically patterned paper sheets.