Bayesian identification and model comparison for random property fields derived from material microstructure

Abstract

This paper provides a Bayesian framework for determining the spatial variability of the apparent material properties of two-phase composites. Bayesian analysis is applied to learn the parameters of the random fields that characterize the mesoscale material properties using computer-simulated images of the material microstructure. The information from such images is used to define the likelihood function of the random field parameters given the homogenized microscale data. The uncertainty in the parameter estimates is quantified through determining their full posterior distribution instead of a point estimate by application of an adaptive sampling algorithm. In addition, the Bayesian approach allows for assessing the plausibility of different correlation models belonging to the Matérn class through computing their respective marginal likelihoods for various choices of the smoothness parameter. The framework is applied to a composite material with large inclusion/matrix stiffness ratio and useful conclusions are derived with regard to the most appropriate correlation model and its parameters.