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A thermo-mechanical continuum theory with internal length for cohesionless granular materials. Part I. A class of constitutive models

Fang, Chung and Wang, Yongqi and Hutter, Kolumban (2006):
A thermo-mechanical continuum theory with internal length for cohesionless granular materials. Part I. A class of constitutive models.
In: Continuum Mechanics and Thermodynamics, Springer, pp. 545-576, 17, (8), ISSN 0935-1175,
[Online-Edition: http://www.springerlink.com/content/v83202545661730w/],
[Article]

Abstract

A thermodynamically consistent continuum theory for single-phase, single-constituent cohesionless granular materials is presented. The theory is motivated by dimensional inconsistencies of the original Goodman-Cowin theory 1-3; it is constructed by removing these inconsistencies through the introduction of an internal length l. Four constitutive models are proposed and discussed in which l is (i) a material constant (Model I), (ii) an independent constitutive variable (Model II), (iii) an independent dynamic field quantity (Model III) and (iv) an independent kinematic field quantity (Model IV). Expressions of the constitutive variables emerging in the systems of the balance equations in these four models in thermodynamic equilibrium are deduced by use of a thermodynamic analysis based on the Müller-Liu entropy principle. Comments on the validity of these four models are given and discussed; the results presented in the current study show a more general formulation for the constitutive quantities and can be used as a basis for further continuum-based theoretical investigations on the behaviour of flowing granular materials. Numerical results regarding simple plane shear flows will be discussed and compared in Part II of this work.

Item Type: Article
Erschienen: 2006
Creators: Fang, Chung and Wang, Yongqi and Hutter, Kolumban
Title: A thermo-mechanical continuum theory with internal length for cohesionless granular materials. Part I. A class of constitutive models
Language: English
Abstract:

A thermodynamically consistent continuum theory for single-phase, single-constituent cohesionless granular materials is presented. The theory is motivated by dimensional inconsistencies of the original Goodman-Cowin theory 1-3; it is constructed by removing these inconsistencies through the introduction of an internal length l. Four constitutive models are proposed and discussed in which l is (i) a material constant (Model I), (ii) an independent constitutive variable (Model II), (iii) an independent dynamic field quantity (Model III) and (iv) an independent kinematic field quantity (Model IV). Expressions of the constitutive variables emerging in the systems of the balance equations in these four models in thermodynamic equilibrium are deduced by use of a thermodynamic analysis based on the Müller-Liu entropy principle. Comments on the validity of these four models are given and discussed; the results presented in the current study show a more general formulation for the constitutive quantities and can be used as a basis for further continuum-based theoretical investigations on the behaviour of flowing granular materials. Numerical results regarding simple plane shear flows will be discussed and compared in Part II of this work.

Journal or Publication Title: Continuum Mechanics and Thermodynamics
Volume: 17
Number: 8
Publisher: Springer
Uncontrolled Keywords: Goodman-Cowin theory; Müller-Liu entropy principle; Internal length; Granular materials
Divisions: 16 Department of Mechanical Engineering > Fluid Dynamics (fdy)
16 Department of Mechanical Engineering
Date Deposited: 24 Aug 2011 17:58
Official URL: http://www.springerlink.com/content/v83202545661730w/
Additional Information:

doi:10.1007/s00161-006-0007-8

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