Universal Strain Correlations in Amorphous Solids

Abstract

The plastic deformation of amorphous solids is primarily driven by the localized re arrangement or shear transformation of individual particles, which interact with one another through long-range elastic strain fields. Understanding the spatial and tempo ral organization of these rearrangements is essential for comprehending the transition from elastic to plastic deformation. While we have made significant progress in under standing this phenomenon at low temperatures and under quasi-static deformation conditions, our comprehension remains limited when it comes to finite deformation rates and temperatures. In the following work, we present evidence that interactions between these rear rangements give rise to consistent patterns of strain distribution in amorphous solids subjected to shear stress. Through a combination of experiments and simulations, we have uncovered a specific quadrupolar symmetry in the strain correlations. This symmetry resembles the strain field produced by an Eshelby inclusion, a concept from materials science. However, unlike the Eshelby field, these correlations exhibit a decay pattern characterized by 1/rα, where the exponent α gradually shifts from 3 to 1 as the system progresses from the linear elastic regime to a state of steady-state plastic flow. We have further explained these findings by modeling the particles undergoing shear transformations or rearrangements as if they were Eshelby inclusions. Initially, at small strains, the plastic rearrangements appear isolated from each other. How ever, as the applied strain increases, these rearrangements start to cluster together, and their average size expands. Ultimately, this clustering phenomenon leads to the system yielding and entering a state of plastic flow. Our study underscores the importance of density correlations among these plastic rearrangements and demonstrates how universal patterns of strain distribution emerge at different stages of the elasto-plastic deformation process.