Emergent scales and spatial correlations at the yielding transition of glassy materials

TL;DR

This paper models the yielding transition in glassy materials, revealing how disorder influences the nature of the transition and the emergence of a correlation length that characterizes dynamic heterogeneities.

Contribution

It introduces a lattice model that captures the impact of disorder on the yielding transition, linking it to phase transition phenomena and revealing the role of a correlation length.

Findings

Disorder changes the transition from discontinuous to continuous.

A correlation length $\xi$ emerges and diverges as disorder vanishes.

Yielding's abruptness is related to a lengthscale of heterogeneities.

Abstract

Glassy materials yield under large external mechanical solicitations. Under oscillatory shear, yielding shows a well-known rheological fingerprint, common to samples with widely different microstructures. At the microscale, this corresponds to a transition between slow, solid-like dynamics and faster liquid-like dynamics, which can coexist at yielding in a finite range of strain amplitudes. Here, we capture this phenomenology in a lattice model with two main parameters: glassiness and disorder, describing the average coupling between adjacent lattice sites, and their variance, respectively. In absence of disorder, our model yields a law of correspondent states equivalent to trajectories on a cusp catastrophe manifold, a well-known class of problems including equilibrium liquid-vapour phase transitions. Introducing a finite disorder in our model entails a qualitative change, to a continuous and rounded transition, whose extent is controlled by the magnitude of the disorder. We show that a spatial correlation length $\xi$ emerges spontaneously from the coupling between disorder and bifurcating dynamics. With vanishing disorder, $\xi$ diverges and yielding becomes discontinuous, suggesting that the abruptness of yielding can be rationalized in terms of a lengthscale of dynamic heterogeneities.