Uni-axial deformation of a random packing of particles

Arch. Appl. Mech., 1999, Vol 69, 181-203.

J. Jäger, Blattwiesenstr. 7, 76227 Karlsruhe

 Keywords: Granular material, generalized Hertz contact, elastic friction, nonlinear, elasticity

Abstract: The mechanical behavior of a dense packing of spheres with small irregularities is investigated in this paper. A generalization of the hertzian contact model for surfaces of the form xk yields a normal contact force Fn, which is proportional to z1+1/k, with the normal displacement z. For oblique forces, the frictional force can be calculated with a theory by Jäger. Different load cases are explained in detail. It is shown that the stress-strain curve during initial  loading of the packing is identical with the force-displacement relation at the contact point, using an appropriate constant. The results for uniaxial loading, unloading and reloading are illustrated. As experimentally observed,  the axial pressure of the unloading process is smaller than during loading, while the lateral pressure increases. The stress- strain  relation is compared with well known empirical relations of rock and soil mechanics, and the  wave velocity for spherical irregularities agrees with earlier geomechanical theories for a random packing of smooth spheres.