Image-based random fields in numerical modeling of heterogeneous materials

Abstract

Modeling of spatial variability using random fields is nowadays standard in computational modeling of heterogeneous materials. The only difficulty remains in determining the input parameters of the random field in order to represent the modeled material morphology as accurately as possible. The most frequent method of constructing a random field relies on various covariance kernels that primarily use as input the values of the correlation lengths, which are typically estimated ad-hoc. However, another possibility is to extract input parameters from the modeled material morphology. Moreover, this approach enables to calculate the covariance kernel itself. The performance of the image-based procedure is compared with standard methods of random field construction on the response of the two-phase elastic material.

Keywords

• Karhunen-Loève expansion
• random field
• Monte Carlo
• two-phase elastic material