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A thermo-mechanical continuum theory with internal length for cohesionless granular materials. Part II. Non-equilibrium postulates and numerical simulations of simple shear, plane Poiseuille and gravity driven problems

Fang, Chung and Wang, Yongqi and Hutter, Kolumban (2006):
A thermo-mechanical continuum theory with internal length for cohesionless granular materials. Part II. Non-equilibrium postulates and numerical simulations of simple shear, plane Poiseuille and gravity driven problems.
In: Continuum Mechanics and Thermodynamics, Springer, pp. 577-607, 17, (8), ISSN 0935-1175, [Online-Edition: http://www.springerlink.com/content/vr31t277xg750477/],
[Article]

Abstract

This article continues Part I. Here the non-equilibrium responses of the constitutive variables t (Cauchy stress tensor), q (heat flux vector), h (equilibrated stress vector), Γ (flux term associated with the internal length l), Π (production term associated with l) and f (equilibrated intrinsic body force) as well as the Helmholtz free energy Ψ are postulated by use of a quasi-linear theory for three of four models deduced in Part I. In so doing, together with the equilibrium responses gained in Part I, a complete set of constitutive equations for the constitutive quantities for each model is obtained. The implemented models are applied to investigate typical isothermal steady granular shearing flows with incompressible grains, namely, simple plane shear flow, inclined gravity-driven flow and vertical channel-flow. The emphasis is on the models in which l is considered a material constant (Model I) and an independent dynamic field quantity (Model III). Numerical results show that Model III is more appropriate than Model I since in the former model the effect of the motion of an individual grain can better be taken into account. Such a result is in particular significant for avalanches, since it verifies the existence of a thin layer immediately above the base of an avalanche, in which the grains are colliding strongly with one another, and provides a quantitative means to measure such a thin layer.

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 II. Non-equilibrium postulates and numerical simulations of simple shear, plane Poiseuille and gravity driven problems
Language: English
Abstract:

This article continues Part I. Here the non-equilibrium responses of the constitutive variables t (Cauchy stress tensor), q (heat flux vector), h (equilibrated stress vector), Γ (flux term associated with the internal length l), Π (production term associated with l) and f (equilibrated intrinsic body force) as well as the Helmholtz free energy Ψ are postulated by use of a quasi-linear theory for three of four models deduced in Part I. In so doing, together with the equilibrium responses gained in Part I, a complete set of constitutive equations for the constitutive quantities for each model is obtained. The implemented models are applied to investigate typical isothermal steady granular shearing flows with incompressible grains, namely, simple plane shear flow, inclined gravity-driven flow and vertical channel-flow. The emphasis is on the models in which l is considered a material constant (Model I) and an independent dynamic field quantity (Model III). Numerical results show that Model III is more appropriate than Model I since in the former model the effect of the motion of an individual grain can better be taken into account. Such a result is in particular significant for avalanches, since it verifies the existence of a thin layer immediately above the base of an avalanche, in which the grains are colliding strongly with one another, and provides a quantitative means to measure such a thin layer.

Journal or Publication Title: Continuum Mechanics and Thermodynamics
Volume: 17
Number: 8
Publisher: Springer
Uncontrolled Keywords: Internal length; Granular materials; Simple shear flows
Divisions: 16 Department of Mechanical Engineering > Fluid Dynamics (fdy)
16 Department of Mechanical Engineering
Date Deposited: 24 Aug 2011 17:59
Official URL: http://www.springerlink.com/content/vr31t277xg750477/
Additional Information:

DOI: 10.1007/s00161-006-0008-7

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