Abstract:
Amorphous solids appear to react elastically to small external strains, but in contrast to ideal elastic media,
plastic responses abound immediately at any value of the strain. Such plastic responses are quasilocalized in
nature, with the “cheapest” one being a quadrupolar source. The existence of such plastic responses results
in screened elasticity in which strains and stresses can either quantitatively or qualitatively differ from the
unscreened theory, depending on the specific screening mechanism. Here we offer a theory of such screening
effects by plastic quadrupoles, dipoles, and monopoles, explain their natural appearance, and point out the
analogy to electrostatic screening by electric charges and dipoles. For low density of quadrupoles the effect
is to normalize the elastic moduli without a qualitative change compared to pure elasticity theory; for higher
density of quadrupoles the screening effects result in qualitative changes. Predictions for the spatial dependence
of displacement fields caused by local sources of strains are provided and compared to numerical simulations.
We find that anomalous elasticity is richer than electrostatics in having a screening mode that does not appear in
the electrostatic analog.
