Simulations of Non-Gaussian Property Fields Based on the Apparent Properties of Statistical Volume Elements

Abstract

The properties of composite materials with random microstructures are often defined by homogenizing the properties of a representative volume element (RVE). This results in the effective properties of an equivalent homogeneous material. This approach is useful for predicting a global response but smooths the underlying variability of the composite's properties resulting from the random microstructure. Statistical volume elements (SVEs) are partitions of an RVE. Homogenization of individual SVEs produces a population of apparent properties. While not as rigorously defined as RVEs, SVEs can still provide a repeatable framework to characterize mesoscale variability in composite properties. In particular, their statistical properties can be used as the basis for simulation studies. For this work, Voronoi tessellation was used to partition RVEs into SVEs and apparent properties developed for each SVE. The resulting field of properties is characterized with respect to its spatial autocorrelation and distribution. These autocorrelation and distribution functions (PDFs) are then used as target fields to simulate additional property fields, with the same probabilistic characteristics. Simulations based on SVEs may provide a method of further exploring the uncertainty within the underlying approximations or of highlighting effects that might be experimentally measurable or used to validate the use of an SVE mesoscale analysis in a specific predictive model. This work presents an update to an existing simulation technique developed by Joshi (1975, “A Class of Stochastic Models for Porous Media,” Ph.D. thesis, University of Kansas, Lawrence, KS) and initially extended by Adler et al. (1990, “Flow in Simulated Porous Media,” Int. J. Multiphase Flow, 16(4), pp. 691–712). The simulation methodology is illustrated for three random microstructures and two SVE partitioning sizes.