A set-based approach is presented for solving multi-scale or multi-level design problems. The approach incorporates Bayesian network classifiers (BNC) for mapping design spaces at each level and flexibility metrics for intelligently narrowing the design space as the design process progresses. The approach is applied to a hierarchical composite materials design problem, specifically, the design of composite materials with macroscopic mechanical stiffness and loss properties surpassing those of conventional composites. This macroscopic performance is achieved by embedding small volume fractions of negative stiffness (NS) inclusions in a host material. To design these materials, the set-based, multilevel design approach is coupled with a hierarchical modeling strategy that spans several scales, from the behavior of microscale NS inclusions to the effective properties of a composite material containing those inclusions and finally to the macroscopic performance of components. The approach is shown to increase the efficiency of multi-level design space exploration, and it is particularly appropriate for top-down, performance-driven design, as opposed to bottom-up, trial-and-error modeling. The design space mappings also build intuitive knowledge of the problem and promising regions of the design space, such that it is almost trivial to identify designs that yield preferred system-level performance.

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