Anomalous Elasticity and Screening in Amorphous Solids

TL;DR

This paper develops a theory of screening effects in amorphous solids caused by plastic quadrupoles, revealing how these effects modify elastic responses and lead to richer phenomena than electrostatic analogies.

Contribution

It introduces a comprehensive theory of elastic screening in amorphous solids due to plastic quadrupoles, dipoles, and monopoles, highlighting their natural emergence and impact on elasticity.

Findings

Screening effects normalize elastic moduli at low quadrupole densities.

Higher quadrupole densities cause qualitative changes in elastic behavior.

Predicted displacement fields match numerical simulations.

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 quasi-localized in nature, with the ``cheapest" one being a quadrupolar source. The existence of such plastic responses results in {\em screened elasticity} in which strains and stresses can either quantitatively or qualitatively differ from the un-screened 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