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.
Similar content being viewed by others
References
Grigoriu M. Crossings of non-Gaussian translation processes. Journal of Engineering Mechanics, 1984, 110(4): 610–620
Grigoriu M. Random field models for two-phase microstructures. Journal of Applied Physics, 2003, 94(6): 3762–3770
Yeong C L Y, Torquato S. Reconstructing random media. Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 1998, 57(1): 495–506
Patelli E, Schuëller G I. Computational optimization strategies for the simulation of random media and components. Computational Optimization and Applications, 2012, 53(3): 903–931
Koutsourelakis P S, Deodatis G. Simulation of binary random fields with applications to two-phase random media. Journal of Engineering Mechanics, 2005, 131(4): 397–412
Sethian J. Level set methods and fast marching methods: Evolving interfaces in computational geometry, fluid mechanics, computer vision and materials science. Cambridge: Cambridge University Press, 1999, 218–225
Ostoja-Starzewski M. Random field models of heterogeneous materials. International Journal of Solids and Structures, 1998, 35(19): 2429–2455
Gioffrè M, Gusella V. Peak response of a nonlinear beam. Journal of Engineering Mechanics, 2007, 133(9): 963–969
Arwade S R, Grigoriu M. Probabilistic model for polycrystalline microstructures with application to intergranular fracture. Journal of Engineering Mechanics, 2004, 130(9): 997–1005
Grigoriu M. Simulation of stationary non-Gaussian translation processes. Journal of Engineering Mechanics, 1998, 124(2): 121–126
Shields M D, Deodatis G, Bocchini P. A simple and efficient methodology to approximate a general non-Gaussian stationary stochastic process by a translation process. Probabilistic Engineering Mechanics, 2011, 26(4): 511–519
Deodatis G, Micaletti R C. Simulation of highly skewed non-Gaussian stochastic processes. Journal of Engineering Mechanics, 2001, 127(12): 1284–1295
Lagaros N D, Stefanou G, Papadrakakis M. An enhanced hybrid method for the simulation of highly skewed non-Gaussian stochastic fields. Computer Methods in Applied Mechanics and Engineering, 2005, 194(45–47): 4824–4844
Shinozuka M, Deodatis G. Simulation of stochastic processes by spectral representation. Applied Mechanics Reviews, 1991, 44(4): 191–203 (ASME)
Ghanem R, Spanos P D. Stochastic finite elements: A spectral approach. Berlin: Springer-Verlag, 1991
Graham-Brady L, Xu X F. Stochastic morphological modeling of random multiphase materials. Journal of Applied Mechanics, 2008, 75(6): 061001
Feng J W, Li C F, Cen C, Owen D R J. Statistical reconstruction of two-phase random media. Computers & Structures, 2014, 137: 78–92
Ferrante F J, Arwade S R, Graham-Brady L L. A translation model for non-stationary, non-Gaussian random processes. Probabilistic Engineering Mechanics, 2005, 20(3): 215–228
Jiao Y, Stillinger F H, Torquato S. A superior descriptor of random textures and its predictive capacity. Proceedings of the National Academy of Sciences of the United States of America, 2009, 106(42): 17634–17639
Savvas D, Stefanou G, Papadrakakis M, Deodatis G. Homogenization of random heterogeneous media with inclusions of arbitrary shape modelled by XFEM. Computional Mechanics, 2014, DOI: 10.1007/s00466-014-1053-x
Debye P, Bueche M. Scattering by an inhomogeneous solid. Journal of Applied Physics, 1949, 20(6): 518–525
Adler P M, Jacquin C G, Quiblier J A. Flow in simulated porous media. International Journal of Multiphase Flow, 1990, 16(4): 691–712
Stefanou G, Nouy A, Clément A. Identification of random shapes from images through polynomial chaos expansion of random level set functions. International Journal for Numerical Methods in Engineering, 2009, 79(2): 127–155
Zhao X, Duddu R, Bordas S P A, Qu J. Effects of elastic strain energy and interfacial stress on the equilibrium morphology of misfit particles in heterogeneous solids. Journal of the Mechanics and Physics of Solids, 2013, 61(6): 1433–1445
Sonon B, François B, Massart T J. A unified level set based methodology for fast generation of complex microstructural multiphase RVEs. Computer Methods in Applied Mechanics and Engineering, 2012, 223–224: 103–122
Hiriyur B, Waisman H, Deodatis G. Uncertainty quantification in homogenization of heterogeneous microstructures modelled by XFEM. International Journal for Numerical Methods in Engineering, 2011, 88(3): 257–278
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Stefanou, G. Simulation of heterogeneous two-phase media using random fields and level sets. Front. Struct. Civ. Eng. 9, 114–120 (2015). https://doi.org/10.1007/s11709-014-0267-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11709-014-0267-5