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Elasticity in Amorphous Solids: Nonlinear or Piecewise Linear?

Awadhesh K Dubey1, Itamar Procaccia1, Carmel A B Z Shor1

  • 1Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel.

Physical Review Letters
|March 12, 2016
PubMed
Summary
This summary is machine-generated.

Mechanical behavior in amorphous solids shows a piecewise linear elastic response, not nonlinear. Reconsidering nonlinear expansions at low temperatures reveals differences between quenched and annealed averages for stress-strain curves.

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Area of Science:

  • Solid Mechanics
  • Materials Science
  • Statistical Physics

Background:

  • Macroscopic amorphous solids exhibit nonlinear-looking stress-strain curves under quasistatic strain-controlled measurements.
  • These curves terminate in mechanical collapse or a steady state with constant mean stress despite increasing strain.
  • Nonlinear expansions of stress in powers of strain are often tempting but may misrepresent the underlying physics at low temperatures.

Purpose of the Study:

  • To challenge the interpretation of nonlinear stress-strain curves in amorphous solids.
  • To highlight the importance of considering quenched versus annealed averages.
  • To propose an alternative, more accurate description of the elastic response.

Main Methods:

  • Analysis of quasistatic strain-controlled measurements.
  • Theoretical evaluation of a stress-dependent shear modulus.
  • Comparison of quenched and annealed averages of stress-strain data.

Main Results:

  • The elastic response of amorphous solids is fundamentally piecewise linear, not inherently nonlinear.
  • A significant difference exists between quenched and annealed averages of stress-strain curves.
  • A stress- or strain-dependent shear modulus provides a more accurate description.

Conclusions:

  • Nonlinear expansions for stress-strain relationships in amorphous solids are misleading at low temperatures.
  • The mechanical response is better characterized by a piecewise linear elastic model using a strain-dependent shear modulus.
  • Understanding the distinction between quenched and annealed states is crucial for accurate material modeling.