Tungsten Sphere 3D Particle-Packed Cube
It is well known that the size and distribution of the solids (mainly spheres) within the cavity determine the overall density of the cavity. Thus, cavities filled with a matrix of sintered tungsten solids and tungsten powder represent a breakthrough in the evolution of this new technology. This solution is cost effective, flexible, easy to assemble, and the material reusable.
Early attempts at three-dimensional calculations used a regular bimodal array of spheres, but some of the surfaces created were physically unrealistic. Thus, a three-dimensional packing algorithm was developed. The basic tenets of this algorithm are the following:
- the particles are treated as spheres
- the spheres can have various sizes, with the size distribution defined by experimental data
- the algorithm uses a concurrent packing strategy
The packing algorithm is one of the most significant breakthroughs in achieving maximum 3D density. Below is an example generated by the packing algorithm:
The concurrent method differs from the sequential method, where each sphere is placed inside the cube one at a time, most likely via a Monte-Carlo method, with special care so as not to have any two spheres lie inside one another. The difference in the concurrent method is that all spheres are placed randomly within a periodic cube with an assigned random velocity, but with zero initial radius. As time evolves, the spheres grow linearly in time and move in the direction as dictated by their velocities. When two spheres collide, they are repelled using classical collision dynamics.
The algorithm stops when either a desired packing fraction (defined as the ratio of the total sphere volume to total cube volume) is achieved, or when the pack becomes jammed.
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