### 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, ν^{eff}, of such a mixture is a convex function of the volume fraction, so that ν^{eff} 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 language | English |
---|---|

Pages (from-to) | 172-180 |

Number of pages | 9 |

Journal | Journal of Applied Mechanics, Transactions ASME |

Volume | 66 |

Issue number | 1 |

Publication status | Published - Mar 1999 |

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### ASJC Scopus subject areas

- Mechanics of Materials
- Computational Mechanics

### Cite this

*Journal of Applied Mechanics, Transactions ASME*,

*66*(1), 172-180.

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

Research output: Contribution to journal › Article

*Journal of Applied Mechanics, Transactions ASME*, vol. 66, no. 1, pp. 172-180.

}

TY - JOUR

T1 - On a spring-network model and effective elastic moduli of granular materials

AU - Alzebdeh, K.

AU - Ostoja-Starzewski, M.

PY - 1999/3

Y1 - 1999/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0033097871&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033097871&partnerID=8YFLogxK

M3 - Article

VL - 66

SP - 172

EP - 180

JO - Journal of Applied Mechanics, Transactions ASME

JF - Journal of Applied Mechanics, Transactions ASME

SN - 0021-8936

IS - 1

ER -