Hernan Makse Research on Nonlinear Elasticity of Granular Aggregates--- Schlumberger-Doll Research

  • NONLINEAR ELASTICITY OF GRANULAR MATTER (a pdf presentation)

    We have begun a numerical study of the acoustic properties of weakly consolidated granular materials. Using a discrete element (molecular dynamics) code originally developed by Cundall, we are able to calculate the elastic properties of a disordered array of spherical grains. These grains interact with one another via (1) non-linear Hertz (longitudinal) contact forces and (2) friction generated transverse forces.

    Numerical work in this area is needed because analytic theories based on Hertz contacts are not fully consistent with the available experimental data. Experiments on isotropic compression of a granular assembly of spheres show that the shear and bulk moduli vary with the confining pressure, P, faster than the 1/3 power law predicted by contact theory. Moreover, the ratio between the experimental bulk and shear moduli is found to be constant (i.e. pressure independent) but with a value larger than the prediction of the Hertzian theory.

    Our numerical simulations treat a deforming granular assembly of spheres under isotropic loading with periodic boundary conditions. Our results for the behavior of the elastic moduli of the system show a dependence on the pressure and a value of the ratio of the elastic moduli which agree well with experiments.

    Our current efforts are focused in the following areas: to develop a more sophisticated analytic nonlinear elasticity theory, and to describe the elasticity of particulate systems under the framework of statistical mechanics of jamming. See recent paper in postscript or pdf version.

  • Force chains in granular aggregates

    An example of force chains can be observed below. This is a result of a molecular dynamics simulations of an assembly of spherical grains interacting via Hertzian contact forces and tangential frictional forces. The system is being compressed in the vertical direction and extended in the horizontal (y) direction (shear test). Notice the normal force chains aligned in the vertical (red sticks) and horizontal directions (green sticks).

  • Collaborators

    Larry Schwartz and Dave Johnson (Schlumberger-Doll Research), Jim Jenkins (Cornel University).

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