solidspheres

Solidspheres are rigid, solid, non-porous spheres used as model particles in physics, materials science, and computational simulations. The term describes spheres that are assumed to have no internal voids and to interact through contact forces when they touch, as opposed to hollow shells or porous particles.

Geometrically, a solidsphere has a radius r, volume V = 4/3 π r^3, and surface area A = 4 π r^2. If the material density is ρ, its mass is m = ρV. The inertia and dynamic response of a solidsphere depend on these geometric and material properties. In many models, solidspheres are treated as rigid bodies with a specified coefficient of restitution and friction.

Interactions between solidspheres are governed by contact mechanics. Elastic spheres commonly follow Hertzian contact theory for the normal force during compression, while tangential forces are described by friction laws, often incorporating a friction coefficient. Realistic models may include rolling resistance, cohesive forces, and deformation at contact points to capture behavior under load, vibration, or shear.

Applications of solidspheres include discrete element method (DEM) simulations of granular materials, calibration standards in metrology, and the design of photonic or phononic crystals where spherical inclusions create periodic structures. They also serve as simple building blocks in theoretical studies of packing, jamming transitions, and flow through hoppers or sieves.

In packing problems, equal-radius solidspheres achieve the densest known three-dimensional arrangement with a packing density of π/√18 ≈ 0.74048 in the face-centered cubic or hexagonal close-packed lattices. Random arrangements typically yield lower densities, with ongoing research into jammed states and coordination statistics. See also sphere, packing problem, discrete element method.