A multi-level upscaling and validation framework for uncertainty quantification in additively manufactured lattice structures
Gorguluarslan, Recep Muhammet
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Multiscale modeling techniques are playing an ever increasing role in the effective design of complex engineering systems including aircraft, automobiles, etc. Lightweight cellular lattice structures (CLSs) gained interest recently since their complex structure, composed of a network of interconnected strut members, can be fabricated by additive manufacturing (AM). However, uncertainties in the fabricated strut members of CLSs are introduced by the layer-by-layer manufacturing process. These fine scale uncertainties influence the overall product performance resulting in inaccurate predictions of reality and increased complexity in simulations. In this research, a multi-level upscaling and validation framework is established that will enable accurate estimation of the performance of AM-fabricated CLSs under uncertainties. An improved stochastic upscaling method based on Polynomial Chaos Expansion (PCE) is employed to quantify and propagate the uncertainties across multiple levels efficiently. The upscaling method is integrated with a hierarchical validation approach to ensure that accurate predictions are made with the homogenized models. The u-pooling method is incorporated with the Kolmogorov-Smirnov test as the validation metric to efficiently use the limited experimental data during validation. The framework is applied to representative examples to demonstrate its efficacy in accurately characterizing the elastic properties of CLSs under uncertainties. The framework is also used to show its applicability in designing CLSs under uncertainties without the use of expensive simulations and optimization processes. The proposed framework is generalized to apply to any complex engineering structure that incorporates computationally intensive simulations and/or expensive experiments associated with fine scale uncertainties.