Numerical Calculation of Two Dimensional Random Packings of Circles

Abstract

Packing fractions and average contact numbers of random packings of circles have been calculated with the Monte-Carlo method simulation by a computer.
Circles were put into a rectangular container in order. The bottom of the container was taken as x axis and circles were put into the container alongy axis. The circles were assumed to be under a static force field along y axis and directed towards the bottom, and to roll down to dynamically stable positions and settle there.
Obtained results were compared with three dimensional packings of spheres and it was considered that our results on two dimensional packings correspond to those on observed packings of steel balls.
Calculations on the random packings of mixtures of circles of two different sizes and of those with normal size distributions of various standard deviations were performed.