https://hal.science/hal-02447357Khristenko, UstimUstimKhristenko Institute for Numerical Mathematics - Department of Mathematics [Munich] - TUM - Technische Universität Munchen - Université Technique de Munich [Munich, Allemagne]Constantinescu, AndreiAndreiConstantinescuLMS - Laboratoire de mécanique des solides - X - École polytechnique - Mines Paris - PSL (École nationale supérieure des mines de Paris) - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche ScientifiqueLe Tallec, PatrickPatrickLe TallecM3DISIM - Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine - LMS - Laboratoire de mécanique des solides - X - École polytechnique - Mines Paris - PSL (École nationale supérieure des mines de Paris) - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche Scientifique - Inria Saclay - Ile de France - Inria - Institut National de Recherche en Informatique et en AutomatiqueOden, J. TinsleyJ. TinsleyOdenICES - Institute for Computational Engineering and Sciences [Austin] - University of Texas at Austin [Austin]Wohlmuth, BarbaraBarbaraWohlmuth Institute for Numerical Mathematics - Department of Mathematics [Munich] - TUM - Technische Universität Munchen - Université Technique de Munich [Munich, Allemagne]A Statistical Framework for Generating Microstructures of Two-Phase Random Materials: Application to Fatigue AnalysisHAL CCSD2020Random heterogeneous materialTwo-phase materialGaussian level-setMatérn covarianceUncertainty quantificationFatigue Analysis[SPI.MECA.MSMECA] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Materials and structures in mechanics [physics.class-ph]Le Tallec, Patrick2020-01-21 15:40:162023-03-24 14:53:142020-01-24 11:25:40enJournal articleshttps://hal.science/hal-02447357/document10.1137/19M1259286application/pdf1Random microstructures of heterogeneous materials play a crucial role in the material macroscopic behavior and in predictions of its effective properties. A common approach to modeling random multiphase materials is to develop so-called surrogate models approximating statistical features of the material. However , the surrogate models used in fatigue analysis usually employ simple mi-crostructure, consisting of ideal geometries such as ellipsoidal inclusions, which generally does not capture complex geometries. In this paper, we introduce a simple but flexible surrogate microstructure model for two-phase materials through a level-cut of a Gaussian random field with covariance of Matérn class. Such parametrization of the covariance function allows for the representation of a few key design parameters while representing the geometry of inclusions in a more general setting for a large class of random heterogeneous two-phase media. In addition to the traditional morphology descriptors such as porosity, size and aspect ratio, it provides control of the regularity of the inclusions interface and sphericity. These parameters are estimated from a small number of real material images using Bayesian inversion. An efficient process of evaluating the samples, based on the Fast Fourier Transform, makes possible the use of Monte-Carlo methods to estimate statistical properties for the quantities of interest in a given material class. We demonstrate the overall framework of the use of the surrogate material model in application to the uncertainty quantification in fatigue analysis, its feasibility and efficiency, and its role in the microstructure design.