Finite-disorder critical point in the yielding transition of elasto-plastic models

TL;DR

This paper provides numerical evidence for a finite-disorder critical point that separates brittle and ductile yielding in amorphous solids, using extensive simulations of elasto-plastic models in 2D and 3D.

Contribution

The study demonstrates the existence of a finite-disorder critical point in elasto-plastic models, clarifying the transition between brittle and ductile yielding regimes.

Findings

Identification of a finite-disorder critical point separating brittle and ductile yielding.

Estimation of critical exponents in 2D and 3D models.

Evidence supporting the critical point as a universal feature across dimensions.

Abstract

Upon loading, amorphous solids can exhibit brittle yielding, with the abrupt formation of macroscopic shear bands leading to fracture, or ductile yielding, with a multitude of plastic events leading to homogeneous flow. It has been recently proposed, and subsequently questioned, that the two regimes are separated by a sharp critical point, as a function of some control parameter characterizing the intrinsic disorder strength and the degree of stability of the solid. In order to resolve this issue, we have performed extensive numerical simulations of athermally driven elasto-plastic models with long-range and anisotropic realistic interaction kernels in two and three dimensions. Our results provide clear evidence for a finite-disorder critical point separating brittle and ductile yielding, and we provide an estimate of the critical exponents in 2D and 3D.