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The quantity that describes the deformation of a body under stress is known as strain. Strain is given as a fractional change in either length, volume, or geometry under tensile, volume (also known as bulk), or shear stress, respectively, and is a dimensionless quantity. The strain experienced by a body under tensile or compressive stress is called tensile or compressive strain, respectively. In contrast, the strain experienced under bulk stress and shear stress is known as volume and shear...
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The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...
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Elastic constants of zero-temperature amorphous solids.

Grzegorz Szamel1

  • 1Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA.

Physical Review. E
|July 19, 2023
PubMed
Summary

This study presents new, explicitly non-negative expressions for elastic constants in amorphous solids. These findings offer a reliable framework for understanding solid stability and sound damping in these materials.

Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Solid Mechanics

Background:

  • Elastic constants determine the mechanical response of solids to stress.
  • Amorphous solids present unique challenges in calculating elastic properties due to nonaffine deformation.
  • Existing theories may predict unphysical negative elastic constants, indicating material instability.

Purpose of the Study:

  • To derive novel expressions for elastic constants of zero-temperature amorphous solids.
  • To ensure these expressions are explicitly non-negative, guaranteeing material stability.
  • To provide a foundation for improved theoretical models of amorphous solids.

Main Methods:

  • Analysis of elastic constants as the difference between Born and nonaffine correction terms.

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  • Derivation of alternative mathematical formulations for these elastic constants.
  • Focus on zero-temperature amorphous solids.

    • Main Results:

    • New expressions for elastic constants are derived that are guaranteed to be non-negative.
    • The derived expressions avoid spurious predictions of negative elastic constants.
    • These formulations offer a more robust understanding of amorphous solid mechanics.

    Conclusions:

    • The derived expressions provide a physically sound basis for calculating elastic constants in amorphous solids.
    • These findings are crucial for developing accurate theories of material stability and sound damping.
    • The work offers a blueprint for future research in amorphous material mechanics.