A Multiscale Design Methodology for Designing Hierarchical Multiscale Systems Considering Random Field Uncertainty

A multiscale design methodology is proposed in this paper to facilitate the design of hierarchical material and product systems with the consideration of random field uncertainty that propagates across multiple length scales. Based on the generalized hierarchical multiscale decomposition pattern in multiscale modeling, a set of computational techniques are developed to manage the complexity of multiscale design under uncertainty. Novel design of experiments and metamodeling strategies are proposed to manage the complexity of propagating random field uncertainty through three generalized levels of transformation: the material microstructure random field, the material property random field, and the probabilistic product performance. Multilevel optimization techniques are employed to find optimal design solutions at individual scales. A hierarchical multiscale design problem that involves a 2-scale (submicro- and miro-scales) material design and a macro-scale product (bracket) design is used to demonstrate the applicability and benefits of the proposed methodology.