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Elastic moduli and vibrational modes in jammed particulate packings.

Hideyuki Mizuno1, Kuniyasu Saitoh2, Leonardo E Silbert3

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Understanding amorphous solids requires considering both affine and nonaffine moduli. Nonaffine modulus (M_N) critically influences elastic response, approaching a constant value near the jamming transition.

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Area of Science:

  • Solid Mechanics
  • Materials Science
  • Statistical Physics

Background:

  • Amorphous solids exhibit inhomogeneous, nonaffine deformation under homogeneous, affine strain.
  • Elastic response is governed by both affine (M_A) and nonaffine (M_N) moduli.
  • Understanding M_N is crucial for accurate elastic modulus (M) prediction.

Purpose of the Study:

  • Investigate bulk (K) and shear (G) moduli in static jammed particulate packings.
  • Elucidate the role of vibrational modes in nonaffine modulus (M_N).
  • Analyze critical behavior of moduli near the jamming transition (φ_c).

Main Methods:

  • Modal decomposition of displacement and force fields.
  • Analysis of vibrational density of states (g(ω)).
  • Study of particulate packings across a range of packing fractions (φ).

Main Results:

  • M_A depends on static structure, while M_N relates to vibrational modes.
  • Near φ_c, M_N approaches a critical value (M_Nc) as M_N - M_Nc ~ ω*, where ω* is a characteristic frequency.
  • Bulk modulus (K_c) is finite (K_Ac - K_Nc > 0), while critical shear modulus (G_c) is zero (G_Ac = G_Nc).

Conclusions:

  • Distinction between K and G at criticality arises from configurational and vibrational properties.
  • Analytical expressions for critical moduli are validated.
  • Nonaffine deformation significantly impacts the elastic behavior of amorphous solids.