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Shearing flows of a dry granular material-hypoplastic constitutive theory and numerical simulations

Fang, Chung and Wang, Yongqi and Hutter, Kolumban :
Shearing flows of a dry granular material-hypoplastic constitutive theory and numerical simulations.
[Online-Edition: http://onlinelibrary.wiley.com/doi/10.1002/nag.525/pdf]
In: International Journal for Numerical and Analytical Methods in Geomechanics, 30 (14) pp. 1409-1437. ISSN 0363-9061
[Article] , (2006)

Official URL: http://onlinelibrary.wiley.com/doi/10.1002/nag.525/pdf

Abstract

In the present study, the Goodman-Cowin theory is extended to incorporate plastic features to construct an elasto-visco-plastic constitutive model for flowing dry granular materials. A thermodynamic analysis, based on the Müller-Liu entropy principle, is performed to derive the equilibrium expressions of the constitutive variables. Non-equilibrium responses are proposed by use of a quasi- linear theory, in particular a hypoplastic-type relation is introduced to model the internal friction and plastic effects. It is illustrated that the Goodman-Cowin theory can appropriately be extended to include frictional effects into the evolution equation of the volume fraction (i.e. the so-called balance of equilibrated force) and the equilibrium expression of the Cauchy stress tensor. The implemented model is applied to investigate conventional steady isothermal granular flows with incompressible grains, namely simple plane shear, inclined gravity-driven and vertical channel-flows, respectively. Numerical results show that the hypoplastic effect plays a significant role in the behaviour of a flowing granular material. The obtained profiles of the velocity and the volume fraction with hypoplastic features are usually sharper and the shear-thinning effect is more significant than that without such plastic effects. This points at the possible wide applicability of the present model in the fields of granular materials and soil mechanics. In addition, the present paper also provides a framework for a possible extension of the hypoplastic theories which can be further undertaken.

Item Type: Article
Erschienen: 2006
Creators: Fang, Chung and Wang, Yongqi and Hutter, Kolumban
Title: Shearing flows of a dry granular material-hypoplastic constitutive theory and numerical simulations
Language: English
Abstract:

In the present study, the Goodman-Cowin theory is extended to incorporate plastic features to construct an elasto-visco-plastic constitutive model for flowing dry granular materials. A thermodynamic analysis, based on the Müller-Liu entropy principle, is performed to derive the equilibrium expressions of the constitutive variables. Non-equilibrium responses are proposed by use of a quasi- linear theory, in particular a hypoplastic-type relation is introduced to model the internal friction and plastic effects. It is illustrated that the Goodman-Cowin theory can appropriately be extended to include frictional effects into the evolution equation of the volume fraction (i.e. the so-called balance of equilibrated force) and the equilibrium expression of the Cauchy stress tensor. The implemented model is applied to investigate conventional steady isothermal granular flows with incompressible grains, namely simple plane shear, inclined gravity-driven and vertical channel-flows, respectively. Numerical results show that the hypoplastic effect plays a significant role in the behaviour of a flowing granular material. The obtained profiles of the velocity and the volume fraction with hypoplastic features are usually sharper and the shear-thinning effect is more significant than that without such plastic effects. This points at the possible wide applicability of the present model in the fields of granular materials and soil mechanics. In addition, the present paper also provides a framework for a possible extension of the hypoplastic theories which can be further undertaken.

Journal or Publication Title: International Journal for Numerical and Analytical Methods in Geomechanics
Volume: 30
Number: 14
Publisher: John Wiley and Sons
Uncontrolled Keywords: Goodman–Cowin theory; hypoplasticity; granular materials; Müller–Liu entropy principle
Divisions: 16 Department of Mechanical Engineering
16 Department of Mechanical Engineering > Fluid Dynamics (fdy)
Date Deposited: 24 Aug 2011 17:58
Official URL: http://onlinelibrary.wiley.com/doi/10.1002/nag.525/pdf
Additional Information:

doi:10.1002/nag.525

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