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Predicting plasticity of amorphous solids from instantaneous normal modes.

Ivan Kriuchevskyi1, Timothy W Sirk2, Alessio Zaccone1,3

  • 1Department of Physics "A. Pontremoli," University of Milan, via Celoria 16, 20133 Milan, Italy.

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We developed a new mathematical model for amorphous solid plasticity using instantaneous normal modes (INMs) to predict stress-strain curves. This approach accurately models glass deformation without needing system relaxation after strain.

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Computational Materials Science

Background:

  • Understanding amorphous solid deformation is crucial for materials science.
  • Existing models often struggle to capture plasticity and the effects of strain on vibrational properties.
  • Nonaffine lattice dynamics (NALD) provides a framework for elasticity and viscoelasticity in glasses.

Purpose of the Study:

  • To present a novel mathematical description of amorphous solid deformation and plasticity.
  • To extend the concept of instantaneous normal modes (INMs) to deformed systems.
  • To analytically predict the stress-strain curve of glasses.

Main Methods:

  • Extending instantaneous normal modes (INMs) to deformed systems.
  • Formulating linear response theory up to large deformations.
  • Computing the strain-dependent tangent shear modulus from vibrational density of states (VDOS) of affinely strained configurations.
  • Utilizing nonaffine lattice dynamics (NALD).

Main Results:

  • The extended INM spectrum of deformed states allows for analytical prediction of the stress-strain curve.
  • Affine strain reveals soft and unstable modes lost in relaxed systems.
  • Good parameter-free quantitative agreement was achieved between predictions and simulations for a polymer glass.

Conclusions:

  • The developed mathematical framework accurately describes amorphous solid plasticity.
  • The method provides a powerful tool for predicting the mechanical behavior of glasses.
  • This work advances the understanding of deformation mechanisms in disordered materials.