Multiscale Modeling &Simulation, Volume 18, Issue 1, Page 21-43, January 2020.
Random 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 microstructure, 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.

中文翻译：

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产生两相随机材料微观结构的统计框架：在疲劳分析中的应用

2020年1月，《多尺度建模与仿真》，第18卷，第1期，第21-43页。
异质材料的随机微观结构在材料的宏观行为及其有效性能的预测中起着至关重要的作用。对随机多相材料进行建模的常用方法是开发近似于材料统计特征的所谓替代模型。但是，疲劳分析中使用的替代模型通常采用简单的微观结构，该微观结构由理想的几何形状（例如椭圆形夹杂物）组成，通常不能捕获复杂的几何形状。在本文中，我们通过对具有Matérn类协方差的高斯随机场进行切分，介绍了一种两相材料的简单但灵活的替代组织结构模型。协方差函数的这种参数化允许表示一些关键的设计参数，同时以更一般的方式表示一大类随机异质两相介质的内含物几何形状。除了诸如孔隙率，尺寸和长宽比之类的传统形态学描述符外，它还可以控制夹杂物界面和球形度的规则性。这些参数是使用贝叶斯反演从少量真实材料图像中估算的。基于快速傅立叶变换的有效评估样品的过程，使得可以使用蒙特卡洛方法来估计给定材料类别中感兴趣量的统计属性。