Statistics of the Elastic Behavior of Granular Materials

Nicolaas P. Kruyt, L. Rothenburg

Research output: Contribution to journalArticleAcademicpeer-review

50 Citations (Scopus)

Abstract

The elastic behaviour of isotropic assemblies of granular materials consisting of two-dimensional, bonded and non-rotating particles is studied from the micromechanical viewpoint. Discrete element simulations have been performed of assemblies of 50,000 particles with various coordination numbers (average number of contacts per particle) and various ratios of tangential to normal stiffness. Statistics, such as mean, standard deviation and probability distribution function, have been computed for geometrical quantities and contact displacements under compressive and shearing loading. A linear relation is observed between the average number of contacts of a particle and its circumference. Average displacements do not conform to (generalised) uniform strain as is often assumed. The probability density functions for normal and tangential displacements are nearly Gaussian. None of the considered energies satisfy an equipartition of energy between normal and tangential modes.
Original languageEnglish
Pages (from-to)4879-4899
Number of pages21
JournalInternational journal of solids and structures
Volume38
Issue number28-29
DOIs
Publication statusPublished - 2001

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Granular Materials
Granular materials
granular materials
Statistics
statistics
Contact
Shearing
Probability distributions
Probability density function
assemblies
Distribution functions
Stiffness
Equipartition
Discrete Elements
Circumference
circumferences
probability distribution functions
Linear Relation
Probability Distribution Function
probability density functions

Keywords

  • Elasticity
  • Granular materials
  • Micromechanics

Cite this

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abstract = "The elastic behaviour of isotropic assemblies of granular materials consisting of two-dimensional, bonded and non-rotating particles is studied from the micromechanical viewpoint. Discrete element simulations have been performed of assemblies of 50,000 particles with various coordination numbers (average number of contacts per particle) and various ratios of tangential to normal stiffness. Statistics, such as mean, standard deviation and probability distribution function, have been computed for geometrical quantities and contact displacements under compressive and shearing loading. A linear relation is observed between the average number of contacts of a particle and its circumference. Average displacements do not conform to (generalised) uniform strain as is often assumed. The probability density functions for normal and tangential displacements are nearly Gaussian. None of the considered energies satisfy an equipartition of energy between normal and tangential modes.",
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Statistics of the Elastic Behavior of Granular Materials. / Kruyt, Nicolaas P.; Rothenburg, L.

In: International journal of solids and structures, Vol. 38, No. 28-29, 2001, p. 4879-4899.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Statistics of the Elastic Behavior of Granular Materials

AU - Kruyt, Nicolaas P.

AU - Rothenburg, L.

PY - 2001

Y1 - 2001

N2 - The elastic behaviour of isotropic assemblies of granular materials consisting of two-dimensional, bonded and non-rotating particles is studied from the micromechanical viewpoint. Discrete element simulations have been performed of assemblies of 50,000 particles with various coordination numbers (average number of contacts per particle) and various ratios of tangential to normal stiffness. Statistics, such as mean, standard deviation and probability distribution function, have been computed for geometrical quantities and contact displacements under compressive and shearing loading. A linear relation is observed between the average number of contacts of a particle and its circumference. Average displacements do not conform to (generalised) uniform strain as is often assumed. The probability density functions for normal and tangential displacements are nearly Gaussian. None of the considered energies satisfy an equipartition of energy between normal and tangential modes.

AB - The elastic behaviour of isotropic assemblies of granular materials consisting of two-dimensional, bonded and non-rotating particles is studied from the micromechanical viewpoint. Discrete element simulations have been performed of assemblies of 50,000 particles with various coordination numbers (average number of contacts per particle) and various ratios of tangential to normal stiffness. Statistics, such as mean, standard deviation and probability distribution function, have been computed for geometrical quantities and contact displacements under compressive and shearing loading. A linear relation is observed between the average number of contacts of a particle and its circumference. Average displacements do not conform to (generalised) uniform strain as is often assumed. The probability density functions for normal and tangential displacements are nearly Gaussian. None of the considered energies satisfy an equipartition of energy between normal and tangential modes.

KW - Elasticity

KW - Granular materials

KW - Micromechanics

U2 - 10.1016/S0020-7683(00)00313-9

DO - 10.1016/S0020-7683(00)00313-9

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JF - International journal of solids and structures

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