Spatial structure of states of self stress in jammed systems

TL;DR

This paper investigates the spatial structure of states of self stress in jammed systems, revealing how local force organizations relate to the elastic properties and bond modifications in disordered spring networks.

Contribution

It introduces a method to associate a unique state of self stress with each bond in a jammed packing and analyzes their spatial structure.

Findings

States of self stress are localized around bonds.

Changing bond strength affects the elastic response.

Spatial structure links to vibrational modes.

Abstract

States of self stress, organizations of internal forces in many-body systems that are in equilibrium with an absence of external forces, can be thought of as the constitutive building blocks of the elastic response of a material. In overconstrained disordered packings they have a natural mathematical correspondence with the zero-energy vibrational modes in underconstrained systems. While substantial attention in the literature has been paid to diverging length scales associated with zero- and finite-energy vibrational modes in jammed systems, less is known about the spatial structure of the states of self stress. In this work we define a natural way in which a unique state of self stress can be associated with each bond in a disordered spring network derived from a jammed packing, and then investigate the spatial structure of these bond-localized states of self stress. This allows for an understanding of how the elastic properties of a system would change upon changing the strength or even existence of any bond in the system.