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Rheological characteristics of solid–fluid transition in dry granular dense flows: A thermodynamically consistent constitutive model with a pressure‐ratio order parameter
Author(s) -
Fang Chung
Publication year - 2009
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.834
Subject(s) - constitutive equation , rheology , phase transition , statistical physics , granular material , thermodynamics , mechanics , flow (mathematics) , mathematics , physics , finite element method , quantum mechanics
Dry granular flows are characterized as quasi‐static, dense and collisional states by the interactions among the grains, which is indexed macroscopically by an internal variable, called the order parameter defined as the square root of the static pressure to the total pressure. The solid–fluid state transition is regarded as a second‐order phase transition process, and is described by a kinematic evolution of the order parameter. The thermodynamic analysis, based on the Müller–Liu entropy principle, is employed to deduce the equilibrium responses of the constitutive equations, while the dynamic responses are postulated on the basis of a quasi‐linear and the second‐order Ginzburg–Landau phase transition theories. The obtained model is applied to study the rheological characteristics of a dry granular dense flow between two infinite parallel plates, of which the results are compared with those from DEM simulations to estimate the model validity. The present study provides a general framework for the theoretical justifications on the thermodynamic consistencies of order‐parameter‐based constitutive models, and can be extended to flows in quasi‐static or collisional states. Copyright © 2009 John Wiley & Sons, Ltd.