Particle pinning suppresses spinodal criticality in the shear-banding instability

Abstract

Strained amorphous solids often fail mechanically by creating a shear-band. It had been understood that the shear banding instability is usefully described as crossing a spinodal point (with disorder) in an appropriate thermodynamic description. It remained contested however whether the spinodal is critical (with divergent correlation length) or not. Here we offer evidence for critical spinodal by using particle pinning. For a finite concentration of pinned particles the correlation length is bounded by the average distance between pinned particles, but without pinning it is bounded by the system size.

Suppression of spinodal instability by disorder in an athermal system

“…Finally, we conclude by saying that when the thermal fluctuation is irrelevant, disorder-induced local fluctuation smeared the spinodal instabilities, and our results established the existence of spinodal-singularity beyond MF. Similar behavior has been seen in simulations of low-disorder RFIM [21], 2D-Ising model [62], and Kob-Andersen model [63].…”

Mechanical Behaviour of Glasses and Amorphous Materials

“…Are there ideas for how such failure can be avoided? Based on the understanding of the nature of the yielding instability, various investigators have proposed the inclusion of pinning centers and micro-alloying as a way of curtailing run away instabilities [96][97][98][99][100][101][102] and thereby make annealed glasses more resistant to brittle failure, and more ductile. More such insights may arise from the development of a unified view of yielding and flow of amorphous solids in the coming years.…”

Finite-dimensional signature of spinodal instability in an athermal hysteretic transition

“…Therefore, the spiky but nondiverging time constant peak at the coercive fields in Figs. 4(a) and 4(b) is the effect of quenched disorder on the mean-field spinodal slowing down [6,13,27,29]. The local fluctuations connected to the random disorder trigger the heterogeneous nucleation before reaching the spinodal point [24][25][26][27][28].…”

“…Therefore, the correlation length of the system would be bounded by the local disorder points, and heterogeneous nucleation sites start to emerge before approaching the spinodal [24][25][26][27][28]. As a result, a suppressed spinodal slowing down associated with a mild finite-size effect is expected to be observed [6,13,29] that may explain such non-mean-field critical exponents. In this article, we investigate spinodal instability using a random field Ising model (RFIM) in the presence of quench disorder and under athermal conditions.…”