On a spring-network model and effective elastic moduli of granular materials

K. Alzebdeh, M. Ostoja-Starzewski

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Two challenges in mechanics of granular media are taken up in this paper: (i) development of adequate numerical discrete element models of topologically disordered granular assemblies, and (ii) calculation of macroscopic elastic moduli of such materials using effective medium theories. Consideration of the first one leads to an adaptation of a spring-network (Kirkwood) model of solid-state physics to disordered systems, which is developed in the context of planar Delaunay networks. The model employs two linear springs: a normal one along an edge connecting two neighboring vertices (grain centers) which accounts for normal interactions between the grains, as well as an angular one which accounts for angle changes between two edges incident onto the same vertex; edges remain straight and grain rotations do not appear. This model is then used to predict elastic moduli of two-phase granular materials - random mixtures of soft and stiff grains - for high coordination numbers. It is found here that an effective Poisson's ratio, νeff, of such a mixture is a convex function of the volume fraction, so that νeff may become negative when the individual Poisson's ratios of both phases are both positive. Additionally, the usefulness of three effective medium theories - perfect disks, symmetric ellipses, and asymmetric ellipses - is tested.

Original languageEnglish
Pages (from-to)172-180
Number of pages9
JournalJournal of Applied Mechanics, Transactions ASME
Volume66
Issue number1
Publication statusPublished - Mar 1999

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Granular materials
granular materials
modulus of elasticity
Elastic moduli
ellipses
Poisson ratio
apexes
Solid state physics
solid state physics
coordination number
assemblies
Volume fraction
Mechanics
interactions

ASJC Scopus subject areas

  • Mechanics of Materials
  • Computational Mechanics

Cite this

On a spring-network model and effective elastic moduli of granular materials. / Alzebdeh, K.; Ostoja-Starzewski, M.

In: Journal of Applied Mechanics, Transactions ASME, Vol. 66, No. 1, 03.1999, p. 172-180.

Research output: Contribution to journalArticle

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