Uncertainty Quantification and Propagation for Multiscale Materials Systems with Agglomeration and Structural Anomalies

Advancements in manufacturing technologies have enabled material system design optimization across multiple length scales. However, microstructural anomalies (defects) that are present at different scales have not been considered comprehensively enough for systems to be robust to manufacturing variations and uncertainties. Addressing these anomalies through uncertainty quantification and propagation frameworks can help in understanding their effects on a part’s response to design engineered components that can withstand various sources of uncertainty. However, the high-dimensional design space of multiscale material systems can make these frameworks computationally intensive and data-demanding. This work presents an efficient bottom-up hierarchical uncertainty quantification and propagation framework bridging multiple scales to establish a design allowable range for material systems at the part-scale. Specifically, the hierarchical sampling framework integrates (i) an innovative microstructure characterization and reconstruction method, (ii) a mechanistic reduced-order model for fast property predictions in high-dimensional microstructural design spaces, and (iii) an efficient copula-based sampling across multiple scales that reduces the sampling budget by 95%. We demonstrate the framework on an additively manufactured polymer nanocomposite material system that exhibits agglomeration defects formed due to attractive forces between nanoparticles at the microscale and structural variations caused by the voids resulting from different processing conditions at the mesoscale.