Probabilistic multiscale simulation: from disordered microstructures to uncertainties on the structural scale

The present study is concerned with simulation strategies for analysis and prediction of uncertainties in the response of structures consisting of materials with randomly disordered microstructures. Different numerical methods are discussed to analyze the propagation of uncertainties across the scales. Starting from the microstructure, methods and measures for the randomized generation of equivalent computational microstructural models are introduced. Approaches for their homogenization are compiled, including a discussion on the necessity of probabilistic assessment as well as the requirements for the further analysis on the structural or at least next higher scale of structural hierarchy. The analysis on the structural scale is based on random field representations of the effective material properties accounting for all intercorrelations between the individual properties as well as their spatial correlation. To formalize the approach, a semantic interoperable data model is defined. The approaches are illustrated on examples including random microheterogeneous materials such as structural foams and discontinuously fibre reinforced plastics, the failure probability of filament wound pressure vessels containing distributed manufacturing induced defects, the fatigue of polycrystalline steels as well as the fracture initiation in nodular cast iron with distributed spherical graphite inclusions.