Abstract
Understanding the relationship between microstructural features and the effective properties is crucial for designing materials with tailored properties. In this study, we present a framework based on probabilistic learning to establish such relationships for two-phase brittle porous materials and complex macroscopic fracture properties such as average energy release rate and created fracture surface. The microstructural features are characterized using novel descriptors that capture both local and global interactions. These include, for the first time, graph-theoretical features describing the connectivity of the pore network in addition to commonly used statistical descriptors such as porosity dispersion and two-point correlation. A hybrid approach to modeling fracture based on Potential-of-Mean-Force formulation of the lattice element method that draws on probing of high energy bonds and quasi-static relaxation for computation efficiency is used to examine fracture and crack propagation in individual realizations of the random porous material. Probabilistic learning through Bayesian Additive Regression Trees (BART) is employed to establish the feature-property relationships and to perform feature selection for model reduction. The results demonstrate that BART provides accurate predictions of both macroscopic elastic and fracture properties, and reduced order models with strong performance in replicating the predictions with the full set of descriptors. The process of model reduction highlights a clear distinction between the dominant features for elastic properties and fracture properties with features describing global characteristics the most dominant for elastic properties, and fracture properties most influenced by features describing local phenomena such as clustering of pores. Global features, while still relevant, become less dominant in predicting fracture behavior, underscoring the importance of localized pore interactions in driving crack propagation and fracture mechanisms.
•Bayesian learning framework unveils feature-effective property relationships.•Graph theoretical features characterize locally impactful microstructure features.•Bayesian surrogates enable feature selection for both linear elastic and fracture mechanics.•Global and local features dominate effective elastic and fracture properties, respectively.