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.

中文翻译：

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学习脆性多孔材料的织构-性能关系：一种具有图论特征的贝叶斯方法


了解微观结构特征与有效特性之间的关系对于设计具有定制特性的材料至关重要。在这项研究中，我们提出了一个基于概率学习的框架，用于建立两相脆性多孔材料和复杂的宏观断裂特性（如平均能量释放速率和形成的断裂表面）的这种关系。微观结构特征使用捕获局部和全局交互的新描述符来表征。这些首次包括描述孔隙网络连通性的图论特征，以及常用的统计描述符，如孔隙度分散和两点相关性。基于晶格元方法的平均力势公式的断裂建模混合方法，该方法利用高能键的探测和准静态弛豫来提高计算效率，用于检查随机多孔材料单个实现中的裂缝和裂纹扩展。通过贝叶斯加法回归树 （BART） 的概率学习被用来建立特征-属性关系并执行特征选择以进行模型缩减。结果表明，BART 提供了宏观弹性和断裂特性的准确预测，以及降阶模型，在用全套描述符复制预测方面具有很强的性能。 模型简化过程突出了弹性特性和断裂特性的主要特征之间的明显区别，其中描述整体特征的特征是弹性特性最主要的特征，而断裂特性受描述局部现象（如孔隙聚集）的特征影响最大。全局特征虽然仍然相关，但在预测裂缝行为方面变得不那么重要，这凸显了局部孔隙相互作用在驱动裂纹扩展和裂缝机制中的重要性。