Hierarchical multiscale materials modeling: Calibration, uncertainty quantification, and decision support

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Tallman, Aaron E.
McDowell, David L.
Wang, Yan
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Computational material models help establish structure-property relationships by simulating properties, and are most effective when physically-based. The length and time scales of each simulation are constrained both by model type and computing power. Significant uncertainty can arise when models attempt to bridge across length and time scales, especially when using different model constructs. Hierarchical multiscale modeling (HMM) links models at different scales by informing parameters and form of higher scale models based on lower scale simulations, which can reduce uncertainty. The combination of diverse information sources in HMMs requires rigorous approaches to evaluate uncertainty propagation. In the pursuit of improved methods for empirical testing and development of model hierarchies, four approaches in which information is coordinated amongst multiple models are presented. (1) In a reconciled top-down and bottom-up approach, a likelihood-based model calibration method is proposed, and bcc Fe crystal plasticity (CP) is used to demonstrate the compatibility of information pathways. (2) A statistical volume element (SVE) ensemble-based homogenization scheme of two models of cartridge brass polycrystal plasticity is used to inform a Bammann-Chiesa-Johnson macroplasticity model with a local variation in parameters. The effects of SVE size and model form on the performance of the homogenization in bridging microstructure variability to macroscale uncertainty are explored. (3) A multiscale model development framework is outlined for the reduced order modeling of mesoscale variability in cartridge brass. The variability in SVE simulations is included with the results of a series of spherical microindentation experiments in a multiscale data collection. An initial study of the modeling involved in connecting the two length scales is performed. (4) In a CP-finite element method (FEM) based Materials Knowledge System model of -Ti, the influence of texture is considered. Texture is parameterized using generalized spherical harmonics. The CP-FEM model is used with polycrystalline SVE-ensembles to calibrate the MKS model across different textures, sampled according to an uncertainty reduction criterion. Results of the work suggest that data collection is an especially critical step in the formulation and deployment of hierarchical multiscale models. The use of bottom-up information in calibrating a multiscale model is shown to be susceptible to bias. A multiscale approach to coarse-grained simulations of polycrystals at the mesoscale is proposed. An approach to automating the data collection for a reduced-order model of microstructure sensitive response is shown to be competitive with manual data selection, prior to full optimization of the automated approach.
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