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Elastic to plastic transition in amorphous solids
H G E Hentschel1, Itamar Procaccia2
1Department of Physics, Emory University, Atlanta, Georgia 30322, USA.
Chaos (Woodbury, N.Y.)
|May 31, 2024
Summary
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.
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.
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