Numerical modeling of disordered mixture using pseudorandom simulations

The electrostatic effective permittivity of samples of three-dimensional random material consisting of equisized spheres is analyzed numerically. The electric field inside a cubical computation domain is calculated by using finite-element method and field calculation software Opera in a supercomputer. The spheres occupy random positions in the cubic computation cell. As the effective permittivity is analyzed numerically, the finite calculation domain makes the structure infinite and periodic. This kind of structure is called pseudorandom material. This study suggests that a relatively small computational domain (around five times the inclusion sphere radius) could be used when modeling random mixture, if the same samples are analyzed using three orthogonal field orientations. The effective permittivity as a function of the volume fraction of inclusions can be described with generalized mixing formula containing a parameter, which is fitted to numerical results.