TY - JOUR

T1 - A thermo-mechanical continuum theory with internal length for cohesionless granular materials

T2 - PPart II. Non-equilibrium postulates and numerical simulations of simple shear, plane Poiseuille and gravity driven problems

AU - Fang, Chung

AU - Wang, Yongqi

AU - Hutter, Kolumban

PY - 2006/7/1

Y1 - 2006/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33745649423&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33745649423&partnerID=8YFLogxK

U2 - 10.1007/s00161-006-0008-7

DO - 10.1007/s00161-006-0008-7

M3 - Article

AN - SCOPUS:33745649423

VL - 17

SP - 577

EP - 607

JO - Continuum Mechanics and Thermodynamics

JF - Continuum Mechanics and Thermodynamics

SN - 0935-1175

IS - 8

ER -