Rigid filler particles in a rubber matrix: effective force constants by multipolar expansion

After reviewing our recently proposed analogy between filled phantom rubbers and the electrostatics of conductors in a dielectric medium, we describe a general and open-ended algorithm for the evaluation of the force constant (=capacity) matrix between spherical filler particles. The method is based on the multipolar expansion of a charge distribution and of its electrostatic potential. Its performance is assessed by applying it to randomly dispersed hard spheres at volume fractions between 0.1 and 0.3.