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Elastic to plastic transition in amorphous solids.

H G E Hentschel1, Itamar Procaccia2

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Summary
This summary is machine-generated.

This study investigates the transition from isolated plastic events to a finite density of quadrupolar events in amorphous solids under mechanical load. It finds that a finite polarizability is necessary for this transition to occur, enabling continuum theories.

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Area of Science:

  • Solid Mechanics
  • Materials Science
  • Continuum Physics

Background:

  • Plasticity in amorphous solids is linked to non-affine quadrupolar events.
  • Developing continuum theories requires understanding the density of these events.
  • Recent work shows quadrupolar field gradients screen elasticity, but require finite quadrupole density.

Purpose of the Study:

  • To explore the transition from isolated to a finite density of plastic events in amorphous solids.
  • To determine the conditions under which a continuum theory of plasticity can be developed.
  • To investigate the role of quadrupolar fields in mechanical response and emergent length scales.

Main Methods:

  • Analysis of analytically soluble examples of mechanical loading.
  • Introduction of polarizability of Eshelby quadrupoles under strain.
  • Investigation of the conditions for the onset of a finite density of quadrupoles.

Main Results:

  • Plasticity in amorphous solids is associated with non-affine quadrupolar events.
  • A transition from zero to finite density of quadrupolar events is possible.
  • Finite polarizability is a prerequisite for the onset of a finite density of quadrupoles.

Conclusions:

  • The development of continuum theories for amorphous solids depends on the finite density of quadrupolar events.
  • Finite polarizability is the critical factor enabling the transition to a regime with a finite density of quadrupoles.
  • This finding is crucial for understanding screening phenomena and emergent length scales in materials.