Simulation of heterogeneous two-phase media using random fields and level sets

Abstract

The accurate and efficient simulation of random heterogeneous media is important in the framework of modeling and design of complex materials across multiple length scales. It is usually assumed that the morphology of a random microstructure can be described as a non-Gaussian random field that is completely defined by its multivariate distribution. A particular kind of non-Gaussian random fields with great practical importance is that of translation fields resulting from a simple memory-less transformation of an underlying Gaussian field with known second-order statistics. This paper provides a critical examination of existing random field models of heterogeneous two-phase media with emphasis on level-cut random fields which are a special case of translation fields. The case of random level sets, often used to represent the geometry of physical systems, is also examined. Two numerical examples are provided to illustrate the basic features of the different approaches.

Keywords

two-phase media / microstructure / random fields / level sets / shape recovery

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Acknowledgements

This work was implemented within the framework of the research project “MICROLINK: Linking micromechanics-based properties with the stochastic finite element method: a challenge for multiscale modeling of heterogeneous materials and structures” - Action “Supporting Postdoctoral Researchers” of the Operational Program “Education and Lifelong Learning” (Action’s Beneficiary: General Secretariat for Research and Technology), and is co-financed by the European Social Fund (ESF) and the Greek State. The provided financial support is gratefully acknowledged by the author. Special thanks are also due to Professor George Deodatis for fruitful discussions on the topic of simulation of heterogeneous media.

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg