  Holes in mechanical metamaterials, quasi-localized plastic events in
amorphous solids, and bound dislocations in a hexatic matter are different
mechanisms of generic stress relaxation in solids. Regardless of the specific
mechanism, these and other local stress relaxation modes are quadrupolar in
nature, forming the foundation for stress screening in solids, similar to
polarization fields in electrostatic media. We propose a geometric theory for
stress screening in generalized solids based on this observation. The theory
includes a hierarchy of screening modes, each characterized by internal length
scales, and is partially analogous to theories of electrostatic screening such
as dielectrics and Debye-H{\"u}ckel theory. Additionally, our formalism
suggests that the hexatic phase, traditionally defined by structural
properties, can also be defined by mechanical properties and may exist in
amorphous materials.

Soft Condensed Matter;Disordered Systems and Neural Networks;Materials Science