Preface SPECIAL ISSUEMULTISCALE MODELING AND UNCERTAINTY QUANTIFICATION OF HETEROGENEOUS MATERIALS

Abstract

The increasing research activity for microand nano-scales over the last decade has significantly shown the need to account for disparate levels of uncertainty from various sources and across scales. Even over-refined deterministic approaches cannot account for the issue; the integration of stochastic and multiscale methodologies is required to provide a rational framework for uncertainty quantification and reliability analysis of heterogeneous materials. Facing the emergence of new advanced engineered materials, accurate stochastic modeling across multiple length scales becomes imperative. The papers for this special issue are included in Volume 9, issues 3 and 4, 2011 of International Journal for Multiscale Computational Engineering and will focus on multiscale modeling and uncertainty quantification of heterogeneous materials. Particular emphasis is given to advanced computational methods which can greatly assist in tackling complex problems of multiscale stochastic material modeling. The papers can be grouped into several thematic topics that include homogenization and computation of effective elastic properties of random composites, development of computational models for large-scale heterogeneous microstructures, stochastic analysis and design of heterogeneous materials, and multiscale models for the simulation of fracture mechanisms in polycrystalline materials. Volume 9, Issue 3 for the special issue consists of five papers that are devoted to the homogenization and computation of effective elastic properties of random composites. M. Kaminski presents a computational strategy for estimation of the homogenized elasticity tensor of fiberreinforced random composites using the stochastic generalized perturbation technique and a response function approach. The uncertainty of the composite appears at the level of the components’ material properties, while its geometry remains deterministic and perfectly periodic. The response function relating to the homogenized tensor and the input random parameter is determined numerically using several deterministic solutions and least squares approximation. A. Jean, F. Willot, S. Cantournet, S. Forest, and D. Jeulin propose a powerful method for deriving both apparent and effective elastic moduli of rubber with carbon black fillers using finite element and fast Fourier transform methods. The complex two-phase microstructure of the material is generated numerically from a mathematical model of its morphology, which is identified by statistical moments from transmission electron microscopy (TEM) images. The role of a non-uniform distribution of heterogeneities on the elastic as well as electrical properties of composites with “infinitely-contrasted” characteristics is studied numerically and compared with available theoretical results in the contribution by F. Willot and D. Jeulin. It is shown that the non-uniform dispersion of heterogeneities in multiscale microstructures can lead to substantially different effective properties as compared to the one-scale Boolean model, particularly at low volume fractions.