Tri-critical behavior in rupture induced by disorder

TL;DR

This paper uncovers a new tri-critical behavior in rupture phenomena of disordered systems, distinguishing regimes with and without precursors, using analytical and numerical models of fiber composites and spring-block systems.

Contribution

It introduces the concept of tri-criticality in rupture behavior due to disorder, highlighting a transition between first- and second-order regimes in fiber composite models.

Findings

Disorder acts as a relevant field leading to tri-criticality.

Identifies a regime with rupture precursors and one without.

Analytical and numerical models confirm the tri-critical behavior.

Abstract

We discover a qualitatively new behavior for systems where the load transfer has limiting stress amplification as in real fiber composites. We find that the disorder is a relevant field leading to tri--criticality, separating a first-order regime where rupture occurs without significant precursors from a second-order regime where the macroscopic elastic coefficient exhibit power law behavior. Our results are based on analytical analysis of fiber bundle models and numerical simulations of a two-dimensional tensorial spring-block system in which stick-slip motion and fracture compete.