K. Alzebdeh et M. Ostoja-starzewski, On a spring-network model and effective elastic moduli of granular materials, J APPL MECH, 66(1), 1999, pp. 172-180
Citations number
25
Categorie Soggetti
Mechanical Engineering
Journal title
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME
Two challenges in mechanics of granular media are taken up in this paper: (
i) development of adequate numerical discrete element models of topological
ly disordered granular assemblies and (ii) calculation of macroscopic elast
ic moduli of such materials using effective medium theories. Consideration
of the first one leads to an adaptation of a spring-network (Kirkwood) mode
l of solid-state physics to disordered systems, which is developed in the c
ontext of planar Delaunay networks. The model! employs two linear springs:
a normal one along an edge connecting two neighboring vertices (grain cente
rs) which accounts for normal interactions between the grains, as well as a
n angular one which accounts for angle changes between two edges incident o
nto the same vertex; edges remain straight and grain rotations do not appea
r This model is then used to predict elastic moduli of two-phase granular m
aterials-random mixtures of soft and stiff grains-for high coordination num
bers. It is found here that an effective Poisson's ratio, nu(eff), Of such
a mixture is a convex function of the volume fraction, so that nu(eff) may
become negative when the individual Poisson's ratios of both phases are bot
h positive. Additionally, the usefulness of three effective medium theories
-perfect disks, symmetric ellipses, and asymmetric ellipses-is tested.