Title: Discrete Eshelby Inclusions in Amorphous Solids

Author (Table Talk): Evan Willmarth, Yale University

Abstract:

The mechanical response of amorphous solids to athermal, quasistatic shear is characterized by stress-strain curves that contain short elastic segments separated by discontinuous stress drops. Previous studies have shown that large collective particle rearrangements occur during these stress drops and in some cases the displacement fields resemble Eshelby-like quadrupoles that occur in continuum elastic materials during deformation. However, for other stress drops, the displacement fields do not resemble Eshelby-like quadrupoles. Why? The aim of this work is to re-formulate the Eshelby inclusion problem for discrete particulate materials and reproduce the non-affine displacement fields that occur during stress drops as a sum of Eshelby-like defects. We focus on jammed granular packings in two dimensions (2D) subjected to boundary-driven simple shear. We decompose the packings into triangular subunits using Voronoi tessellation and consider each triangle as a possible Eshelby inclusion. We model the disorder in the 2D packings (i.e. missing interparticle contacts) as a series of elastic mismatches from an idealized, fully- connected stress-free spring network. We then treat each interparticle contact as a bond in a global truss network to obtain the required local perturbations that would need to be applied to the ideal spring network to match the non-affine displacement field of the disordered packing under a globally applied strain. In future studies, we will extend this methodology to atomic systems in 3D in the presence of thermal fluctuations to gain insight into the non-affine displacement fields and shear band formation that occur in metallic glasses.