  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.
