STATISTICAL REPRESENTATIVE VOLUME ELEMENT FOR PREDICTING THE DIELECTRIC PERMITTIVITY OF RANDOM MEDIA

摘要

When operating homogenization of random media by means of numerical simulations, it is of primary importance to know the precision of the effective property estimated on a bounded domain of a microstructure, and the size of a so-called Representative Volume Element RVE. To solve this problem, a statistical approach was developed, based on the experimental determination of the integral range from numerical simulations. It enables us to relate the variance of the effective permittivity as a function of the volume V of the simulation, or equivalently of the number of small size unbiased simulations. The method is first validated on 2D simulations of an autodual random set, and then applied to simulations of a 3D Boolean random set.