Universal avalanche statistics and triggering close to failure in a mean field model of rheological fracture

TL;DR

This paper presents a mean field model of rheological fracture showing that avalanche statistics near failure follow a universal class, with transient hardening influencing activity and correlations, including aftershocks and foreshocks.

Contribution

It introduces a mean field model incorporating transient hardening and generalized viscoelasticity, revealing universal avalanche behavior near failure.

Findings

Avalanche statistics are invariant to rheology in the quasistatic limit.

Inter-event correlations such as aftershocks and foreshocks emerge due to hardening.

A single universality class describes the critical failure process.

Abstract

The hypothesis of critical failure relates the presence of an ultimate stability point in the structural constitutive equation of materials to a divergence of characteristic scales in the microscopic dynamics responsible for deformation. Avalanche models involving critical failure have determined common universality classes for stick-slip processes and fracture. However, not all empirical failure processes exhibit the trademarks of criticality. The rheological properties of materials introduce dissipation, usually reproduced in conceptual models as a hardening of the coarse grained elements of the system. Here, we investigate the effects of transient hardening on (i) the activity rate and (ii) the statistical properties of avalanches. We find the explicit representation of transient hardening in the presence of generalized viscoelasticity and solve the corresponding mean field model of fracture. In the quasistatic limit, the accelerated energy release is invariant with respect to rheology and the avalanche propagation can be reinterpreted in terms of a stochastic counting process. A single universality class can be defined from such analogy, and all statistical properties depend only on the distance to criticality. We also prove that inter-event correlations emerge due to the hardening --- even in the quasistatic limit --- that can be interpreted as "aftershocks" and "foreshocks".