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Stress correlations in glasses.

Anaël Lemaître1

  • 1Laboratoire Navier, UMR 8205, École des Ponts, IFSTTAR, CNRS, UPE, Champs-sur-Marne, France.

The Journal of Chemical Physics
|September 17, 2018
PubMed
Summary

In disordered solids, anisotropic stress correlations decay at long-range. This 1/r3 decay is a universal feature in glasses, impacting macroscopic stress self-averaging.

Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Disordered solids, such as glasses, exhibit complex mechanical behaviors.
  • Understanding long-range correlations in stress is crucial for predicting material properties.
  • Previous studies have not fully characterized the nature of stress autocorrelation functions in these systems.

Purpose of the Study:

  • To rigorously establish the long-range behavior of stress autocorrelation functions in disordered three-dimensional isotropic solids.
  • To determine the implications of this behavior for macroscopic stress self-averaging in glasses.
  • To provide a theoretical framework for understanding stress correlations in amorphous materials.

Main Methods:

  • Theoretical analysis based on material isotropy and mechanical balance principles.

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  • Derivation of analytical relationships between stress autocorrelation components.
  • Investigation of the decay of local stress fluctuations over spherical domains.

    • Main Results:

    • Anisotropic stress autocorrelation terms decay as 1/r3 at long-range in disordered isotropic solids.
    • This decay is contingent upon normal local stress fluctuations, defined by inverse domain volume decay.
    • The stress autocorrelation matrix is determined by pressure and stress deviator autocorrelations.

    Conclusions:

    • The 1/r3 stress correlation tail is a general feature of glasses, essential for macroscopic stress self-averaging.
    • The findings provide fundamental insights into the statistical mechanics of amorphous solids.
    • This work establishes a new paradigm for understanding mechanical responses in disordered materials.