### 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 language | English |
---|---|

Pages (from-to) | 457-474 |

Number of pages | 18 |

Journal | Continuum Mechanics and Thermodynamics |

Volume | 19 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2008 Feb 1 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

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

### Cite this

*Continuum Mechanics and Thermodynamics*,

*19*(7), 457-474. https://doi.org/10.1007/s00161-007-0064-7

}

*Continuum Mechanics and Thermodynamics*, vol. 19, no. 7, pp. 457-474. https://doi.org/10.1007/s00161-007-0064-7

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Volume-weighted mixture theory for granular materials

AU - Chen, Kuo Ching

AU - Tai, Yih-Chin

PY - 2008/2/1

Y1 - 2008/2/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=38749118976&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38749118976&partnerID=8YFLogxK

U2 - 10.1007/s00161-007-0064-7

DO - 10.1007/s00161-007-0064-7

M3 - Article

VL - 19

SP - 457

EP - 474

JO - Continuum Mechanics and Thermodynamics

JF - Continuum Mechanics and Thermodynamics

SN - 0935-1175

IS - 7

ER -