2018/01/05 by Jordi Baró, Jörn Davidsen · 23 citations
Earth and Planetary Sciences · Engineering · Environmental Science · Mathematics · Physics and Astronomy · #Critical point (mathematics) #Criticality #Dissipation #Dissipative system #Granular flow and fluidized beds #Hardening (computing) #Landslides and related hazards #Materials science #Mathematical analysis #Mathematics #Mechanics #Physics #Quasistatic process #Rheology #Statistical physics #Thermodynamics #Viscoelasticity #Weissenberg number #cond-mat.soft #cond-mat.stat-mech #earthquake and tectonic studies #physics.geo-ph
paper · pdf · doi:10.1103/physreve.97.033002
published in Physical review. E 97(3), 033002 (American Physical Society)
arxiv created 2018/01/05 · openalex publication_date 2018/03/29 · arxiv updated 2018/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 interevent correlations emerge due to the hardening-even in the quasistatic limit-that can be interpreted as "aftershocks" and "foreshocks."