Interplay of Rearrangements, Strain, and Local Structure during Avalanche Propagation

Abstract

Jammed soft disks exhibit avalanches of particle rearrangements under quasistatic shear. We introduce a framework for understanding the statistics of the progression of avalanches. We follow the avalanches (simulated using steepest descent energy minimization) to decompose them into individual localized rearrangements. We characterize the local structural environment of each particle by a machine-learned quantity, softness, designed to be highly correlated with rearrangements, and analyze the interplay between softness, rearrangements, and strain. Local yield strain has long been incorporated into elastoplastic models; here we show that softness provides a useful proxy for local yield strain. Our findings demonstrate that elastoplastic models must take into account the fully tensorial strain field in order to include the effects of changes in local yield strain due to rearrangements and introduce the equations underpinning a structuro-elastoplastic model that includes local softness.

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Plain Language Summary

For over a century, statistical mechanics has successfully distilled overwhelming amounts of information into distributions of a few relevant variables to uncover the microscopic origins of emergent macroscopic behavior. Here, we harness machine learning to bridge the gap between microscopic particle-level physics and macroscopic collective behavior in a deformed disordered solid, demonstrating that machine learning can be exploited to develop theories of thorny many-body physics problems.

A disordered solid such as a glass rod is strong but brittle. When bent, the rod initially deforms via rearrangements in which the constituent particles change neighbors and bonds. As the rod is bent further, rearrangements proliferate and accumulate, leading to fracture. Other disordered solids are ductile, with rearrangements that trigger avalanches that do not lead to fracture. Ultimately, it is the structure of disordered solids that determines the evolution of particle-scale rearrangements—the collective phenomenon of plasticity—which, in turn, determines how disordered materials respond to large-scale deformation.

In crystalline materials, the particle-level structure associated with rearrangements is characterized by easily identified crystal defects, but in disordered solids every particle is in such a defect. Machine-learning methods have proven successful in correlating local structure with rearrangements. We have taken such methods further by developing a blueprint that untangles the interplay of local structure, plastic events, and elasticity to construct a simplified model of plasticity for any disordered solid in which particles can be tracked in time.

This approach should pave the way toward a deeper understanding of ductility and, perhaps someday, the ability to make glass that can be bent or dropped without breaking.