Frictional granular mechanics: A variational approach

R. Holtzman*, D. B. Silin, T. W. Patzek

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


The mechanical properties of a cohesionless granular material are evaluated from grain-scale simulations. Intergranular interactions, including friction and sliding, are modeled by a set of contact rules based on the theories of Hertz, Mindlin, and Deresiewicz. A computer-generated, three-dimensional, irregular pack of spherical grains is loaded by incremental displacement of its boundaries. Deformation is described by a sequence of static equilibrium configurations of the pack. A variational approach is employed to find the equilibrium configurations by minimizing the total work against the intergranular loads. Effective elastic moduli are evaluated from the intergranular forces and the deformation of the pack. Good agreement between the computed and measured moduli, achieved with no adjustment of material parameters, establishes the physical soundness of the proposed model.

Original languageEnglish (US)
Pages (from-to)1259-1280
Number of pages22
JournalInternational Journal for Numerical Methods in Engineering
Issue number10
StatePublished - Mar 5 2010


  • Effective elastic moduli
  • Grain-scale simulations
  • Intergranular friction
  • Micromechanics
  • Principle of least work
  • Quasi-static model

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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