On the equilibrium response of different modeling approaches for the porosity variation in dry granular matter

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Abstract

A selection of models for the variation in porosity in dry granular flows is investigated and compared on the basis of thermodynamic consistency to illustrate their performance and limitations in equilibrium situations. To this end, the thermodynamic analysis, based on the Müller-Liu entropy principle, is employed to deduce the ultimate constitutive equations at equilibrium. Results show that while all the models deliver appropriate equilibrium expressions of the Cauchy stress tensor for compressible grains, the model in which the variation in porosity is treated kinematically yields a spherical stress tensor for incompressible grains. Only the model in which the variation in porosity is modeled by a dynamic equation can give rise to a non-spherical stress tensor at equilibrium. The present study illuminates the validity and thermodynamic justification of the two modeling approaches for the porosity variation in dry granular matter.

Original languageEnglish
Pages (from-to)121-136
Number of pages16
JournalContinuum Mechanics and Thermodynamics
Volume22
Issue number2
DOIs
Publication statusPublished - 2010 Feb 1

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stress tensors
Porosity
Tensors
porosity
Thermodynamics
thermodynamics
constitutive equations
Constitutive equations
Entropy
entropy

All Science Journal Classification (ASJC) codes

  • Materials Science(all)
  • Mechanics of Materials
  • Physics and Astronomy(all)

Cite this

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title = "On the equilibrium response of different modeling approaches for the porosity variation in dry granular matter",
abstract = "A selection of models for the variation in porosity in dry granular flows is investigated and compared on the basis of thermodynamic consistency to illustrate their performance and limitations in equilibrium situations. To this end, the thermodynamic analysis, based on the M{\"u}ller-Liu entropy principle, is employed to deduce the ultimate constitutive equations at equilibrium. Results show that while all the models deliver appropriate equilibrium expressions of the Cauchy stress tensor for compressible grains, the model in which the variation in porosity is treated kinematically yields a spherical stress tensor for incompressible grains. Only the model in which the variation in porosity is modeled by a dynamic equation can give rise to a non-spherical stress tensor at equilibrium. The present study illuminates the validity and thermodynamic justification of the two modeling approaches for the porosity variation in dry granular matter.",
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