A multi-scale spectral stochastic method for homogenization of multi-phase periodic composites with random material properties

In this work a spectral stochastic computational scheme is proposed that links the global properties of multi‐phase periodic composites to the geometry and random material properties of their microstructural components. To propagate the uncertainties associated with the material properties to the microstructural response the scheme benefits from a combination of homogenization theory built into a finite element framework and the spectral representation of uncertainty based on Hermite Chaos where a probabilistic characterization of the solutions to a set of local problems defined on the period cell is first sought. A full stochastic description of the global (effective) properties is then obtained by averaging the solutions to the forgoing set of local problems over the unit cell. A representative subset of results is compared with the results obtained using Monte Carlo simulation to demonstrate the accuracy of the proposed procedure. Copyright © 2010 John Wiley & Sons, Ltd.