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This study presents a new theoretical model for granular material compaction beyond jamming. It accurately predicts solid fraction evolution and bulk modulus without empirical fitting, revealing key compaction mechanisms.

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Area of Science:

  • Physics
  • Materials Science
  • Geophysics

Background:

  • Compaction of deformable granular materials beyond jamming is poorly understood.
  • Existing models rely on empirical strategies or parameter fitting for pressure-solid fraction relationships.

Purpose of the Study:

  • To develop a theoretical model for granular compaction beyond jamming.
  • To accurately map the evolution of solid fraction (ϕ) with confining pressure (P).
  • To understand the fundamental features of compaction from grain connectivity and individual grain behavior.

Main Methods:

  • Coupled discrete-finite element method simulations of deformable frictional grains under compression.
  • Development of a theoretical model based on the micromechanical definition of the granular stress tensor.

Main Results:

  • Solid fraction (ϕ) evolves nonlinearly from the jamming point and asymptotically approaches unity.
  • A parameter-free theoretical model accurately predicts the evolution of ϕ with confining pressure (P).
  • A derived bulk modulus equation shows excellent agreement with numerical data.

Conclusions:

  • The developed theoretical framework explains compaction by considering joint evolution of grain connectivity and single grain behavior.
  • The model provides a fundamental understanding of granular compaction beyond jamming.
  • The approach offers a predictive tool for granular material behavior under compression.