Mechanical and statistical analyses of loaded sphere packings by means of FEM
Results of mechanical analyses of force distributions in loaded sphere packings are presented. The spheres were replaced by mechanically equivalent beams and the calculations of contact forces were carried out by the finite element method (FEM) in the static case. The sphere packings were random and were simulated by an algorithm, which yields highly dense arrangements of spheres in a box. Three quite different packings are considered, one with layers of spheres of different size, the second one is a homogeneous dense random packing and the third consists of big spheres surrounded by many small spheres. The packings are considered under uniaxial load as in the case of pressure applied by a rigid stamp. A statistical analysis of the resulting force magnitudes was carried out. A new probability model was developed to correlate the distribution functions of the force magnitudes with those of the force components based on the Moran and Downtons’s multivariate exponential distribution.