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  • Rapid Communication

Relations between material mechanical parameters and interparticle potential in amorphous solids

Edan Lerner, Itamar Procaccia, Emily S. C. Ching, and H. G. E Hentschel
Phys. Rev. B 79, 180203(R) – Published 28 May 2009
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  • INTRODUCTION
  • YIELDS STRESS AND THE ENERGY DROPS
  • RESULTS AND SCALING THEORY
  • WHEN SCALING FAILS
  • ACKNOWLEDGEMENTS
    • References

    Abstract

    The shear modulus and yield stress of amorphous solids are important material parameters, with the former determining the rate of increase in stress under external strain and the latter being the stress value at which the material flows in a plastic manner. It is therefore important to understand how these parameters can be related to the interparticle potential. Here a scaling theory is presented such that given the interparticle potential, the dependence of the yield stress, and the shear modulus on the density of the solid can be predicted in the athermal limit. It is explained when such prediction is possible at all densities and when it is only applicable at high densities.

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    • Received 25 February 2009

    DOI:https://doi.org/10.1103/PhysRevB.79.180203

    ©2009 American Physical Society

    Authors & Affiliations

    Edan Lerner1, Itamar Procaccia1,2, Emily S. C. Ching2,3, and H. G. E Hentschel4

    • 1Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
    • 2Institute of Theoretical Physics, The Chinese University of Hong Kong, Shatin, Hong Kong
    • 3Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong
    • 4Deparment of Physics, Emory University, Atlanta, Georgia 30322, USA

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    Issue

    Vol. 79, Iss. 18 — 1 May 2009

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    Images

    • Figure 1
      Figure 1
      (Color online) The three different pairwise potentials discussed in this Rapid Communication.Reuse & Permissions
    • Figure 2
      Figure 2
      (Color online) Typical stress-strain curve for a system with N=4096 and k=10 in Eq. (2).Reuse & Permissions
    • Figure 3
      Figure 3
      (Color online) Stress-strain curves averaged over 20 independent runs for an athermal system with N=4096, k=8 (left panel), and k=10 (right panel) as a function of the density, with the density increasing from bottom to top.Reuse & Permissions
    • Figure 4
      Figure 4
      (Color online) r−1∂U(r)∂r in the range of r∊[ρmax−1/2,ρmin−1/2]. The line through the points represents the scaling laws (6).Reuse & Permissions
    • Figure 5
      Figure 5
      (Color online) The same stress-strain curves as in Fig. 3 but with the stress rescaled by ρν, with ν=4.80 for k=8 (upper panel) and ν=5.87 for k=10 (lower panel). The insets demonstrate the density dependence of σY and μ according to ρν.Reuse & Permissions
    • Figure 6
      Figure 6
      (Color online) Left panel: stress-strain curves for potential (8) which has repulsive and attractive parts. Right upper panel: demonstration of the failure of rescaling of the stress-strain curves. Lower panels: σY and ⟨μ⟩ as functions of the density. Note that predictability is regained only for higher densities, the straight line is ρ7.Reuse & Permissions
    • Figure 7
      Figure 7
      (Color online) The pure number Ω as a function of the density for the three potentials discussed in the text. Note that Ω appears to increase with the exponent of the repulsive part of the potential whenever scaling prevails.Reuse & Permissions
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