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Amorphous solids exhibit unique plastic responses that alter their elastic behavior. This study introduces a theory explaining these screening effects, revealing richer anomalous elasticity than electrostatics.

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Solid Mechanics

Background:

  • Amorphous solids display immediate plastic responses to strain, unlike ideal elastic media.
  • These plastic responses are quasi-localized, with quadrupolar sources being the most energetically favorable.
  • The presence of plastic responses leads to screened elasticity, modifying strain and stress behaviors.

Purpose of the Study:

  • To develop a theoretical framework for screening effects in amorphous solids caused by plastic quadrupoles, dipoles, and monopoles.
  • To explain the natural occurrence of these screening mechanisms.
  • To draw parallels between plastic screening and electrostatic screening.

Main Methods:

  • Theoretical modeling of screening effects by plastic quadrupoles, dipoles, and monopoles.
  • Comparison of theoretical predictions with numerical simulations.
  • Analysis of spatial dependence of displacement fields.

Main Results:

  • A theory for screening effects by plastic quadrupoles, dipoles, and monopoles is presented.
  • Low densities of quadrupoles normalize elastic moduli, while higher densities cause qualitative changes.
  • Predictions for displacement fields align with numerical simulation findings.

Conclusions:

  • Screening by plastic multipoles significantly alters the elastic response of amorphous solids.
  • Amorphous solids exhibit anomalous elasticity with unique screening modes not found in electrostatics.
  • The developed theory provides insights into the complex mechanical behavior of disordered materials.