Volume-weighted mixture theory for granular materials

Kuo Ching Chen, Yih-Chin Tai

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

In the present work we treat granular materials as mixtures composed of a solid and a surrounding void continuum, proposing then a continuum thermodynamic theory for it. In contrast to the common mass-weighted balance equations of mass, momentum, energy and entropy for mixtures, the volume-weighted balance equations and the associated jump conditions of the corresponding physical quantities are derived in terms of volume-weighted field quantities here. The evolution equations of volume fractions, volume-weighted velocity, energy, and entropy are presented and explained in detail. By virtue of the second law of thermodynamics, three dissipative mechanisms are considered which are specialized for a simple set of linear constitutive equations. The derived theory is applied to the analysis of reversible and irreversible compaction of cohesionless granular particles when a vertical oscillation is exerted on the system. In this analysis, a hypothesis for the existence of a characteristic depth within the granular material in its closely compacted state is proposed to model the reversible compaction.

Original languageEnglish
Pages (from-to)457-474
Number of pages18
JournalContinuum Mechanics and Thermodynamics
Volume19
Issue number7
DOIs
Publication statusPublished - 2008 Feb 1

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Granular materials
granular materials
Compaction
Entropy
Thermodynamics
Constitutive equations
entropy
continuums
Volume fraction
Momentum
thermodynamics
mass balance
constitutive equations
voids
kinetic energy
oscillations
energy

All Science Journal Classification (ASJC) codes

  • Materials Science(all)
  • Mechanics of Materials
  • Physics and Astronomy(all)

Cite this

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Volume-weighted mixture theory for granular materials. / Chen, Kuo Ching; Tai, Yih-Chin.

In: Continuum Mechanics and Thermodynamics, Vol. 19, No. 7, 01.02.2008, p. 457-474.

Research output: Contribution to journalArticle

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