Frictional granular mechanics: A variational approach

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

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


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
Pages (from-to)1259-1280
Number of pages22
JournalInternational Journal for Numerical Methods in Engineering
Issue number10
Early online date9 Sep 2009
Publication statusPublished - 5 Mar 2010

Bibliographical note

This is the peer reviewed version of the following article: Holtzman, R, Silin, DB & Patzek, TW 2010, 'Frictional granular mechanics: A variational approach', International Journal for Numerical Methods in Engineering, vol. 81, no. 10, pp. 1259-1280 which has been published in final form at This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.

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