Predicting plasticity of amorphous solids from instantaneous normal modes

Revisiting the question of what instantaneous normal modes tell us about liquid dynamics

The lack of a well-defined equilibrium reference configuration has long hindered a comprehensive atomic-level understanding of liquid dynamics and properties. The Instantaneous Normal Mode (INM) approach, which involves diagonalizing the Hessian matrix of potential energy in instantaneous liquid configurations, has emerged as a promising framework in this direction. However, several conceptual challenges remain, particularly related to the approach's inability to capture anharmonic effects. In this study, we present a set of "experimental facts" through a comprehensive INM analysis of simulated systems, including Ar, Xe, N2, CS2, Ga, and Pb, across a wide temperature range from the solid to gas phase. First, we examine the INM density of states (DOS) and compare it to the DOS obtained from the velocity auto-correlation function. We then analyze the temperature dependence of the fraction of unstable modes and the low-frequency slope of the INM DOS in search of potential universal behaviors. Furthermore, we explore the relationship between INMs and other properties of liquids, including the liquid-like to gas-like dynamical crossover and the momentum gap of collective shear waves. In addition, we investigate the INM spectrum at low temperatures as the system approaches the solid phase, revealing a significant fraction of unstable modes even in crystalline solids. Finally, we confirm the existence of a recently discussed cusp-like singularity in the INM eigenvalue spectrum and uncover its complex temperature-dependent behavior, challenging current theoretical models.

Clustering of negative topological charges precedes plastic failure in 3D glasses

The deformation mechanism in amorphous solids subjected to external shear remains poorly understood because of the absence of well-defined topological defects mediating the plastic deformation. The notion of soft spots has emerged as a useful tool to characterize the onset of irreversible rearrangements and plastic flow, but these entities are not clearly defined in terms of geometry and topology. In this study, we unveil the phenomenology of recently discovered, precisely defined topological defects governing the microscopic mechanical and yielding behavior of a model 3D glass under shear deformation. We identify the existence of vortex-like and antivortex-like topological defects within the 3D nonaffine displacement field. The number density of these defects exhibits a significant anticorrelation with the plastic events, with defect proliferation-annihilation cycles matching the alternation of elastic-like segments and catastrophic plastic drops, respectively. Furthermore, we observe collective annihilation of these point-like defects via plastic events, with large local topological charge fluctuations in the vicinity of regions that feature strong nonaffine displacements. We reveal that plastic yielding is driven by several large sized clusters of net negative topological charge, the massive annihilation of which triggers the onset of plastic flow. These findings suggest a geometric and topological characterization of soft spots and pave the way for the mechanistic understanding of topological defects as mediators of plastic deformation in glassy materials.

Scale Separation of Shear-Induced Criticality in Glasses

In a sheared steady state, glasses reach a nonequilibrium criticality called yielding criticality. We report that the qualitative nature of this nonequilibrium critical phenomenon depends on the details of the system and that responses and fluctuations are governed by different critical correlation lengths in specific situations. This scale separation of critical lengths arises when the screening of elastic propagation of mechanical signals is not negligible. We also discuss the determinant of the impact of screening effects from the viewpoint of the microscopic dissipation mechanism.

Enhanced vibrational stability in glass droplets

We show through simulations of amorphous solids prepared in open-boundary conditions that they possess significantly fewer low-frequency vibrational modes compared to their periodic boundary counterparts. Specifically, using measurements of the vibrational density of states, we find that the D ( ω ) ∼ ω 4 law changes to D ( ω ) ∼ ω δ with δ ≈ 5 in two dimensions and δ ≈ 4.5 in three dimensions. Crucially, this enhanced stability is achieved when utilizing slow annealing protocols to generate solid configurations. We perform an anharmonic analysis of the minima corresponding to the lowest frequency modes in such open-boundary systems and discuss their correlation with the density of states. A study of various system sizes further reveals that small systems display a higher degree of localization in vibrations. Lastly, we confine open-boundary solids in order to introduce macroscopic stresses in the system, which are absent in the unconfined system and find that the D ( ω ) ∼ ω 4 behavior is recovered.

Eigenvalue analysis of stress-strain curve of two-dimensional amorphous solids of dispersed frictional grains with finite shear strain

The stress-strain curve of two-dimensional frictional dispersed grains interacting with a harmonic potential without considering the dynamical slip under a finite strain is determined by using eigenvalue analysis of the Hessian matrix. After the configuration of grains is obtained, the stress-strain curve based on the eigenvalue analysis is in almost perfect agreement with that obtained by the simulation, even if there are plastic deformations caused by stress avalanches. Unlike the naive expectation, the eigenvalues in our model do not indicate any precursors to the stress-drop events.