Multiscale analysis and inverse design of uncertain meso-structures (Meso-AID)

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The generation of complex architectured meso-structures has developed at a rapid pace due to major leaps in processing technology. However, the structures generated by such processes are subject to manifold variations: First, the processing conditions induce some scatter in the microstructure which, in turn, results in varying constitutive behavior. Second, the geometry is subject to stochastic variations. These can manifest, e.g., in variable strut diameters, variations in junction morphology, local waviness or random porosities, to name just a few. It is accepted that these uncertainties cannot be ruled out entirely. Therefore, a better understanding of their impact on the effective structural response is required. In order to build the foundations for this, we first target three main pillars that will later be merged: We model such stochastic meso-structures and characterize them using reasonable descriptors of the intrinsic stochasticity. In parallel we develop direct numerical simulations based on recent Fourier-Accelerated Nodal Solvers that will provide data for robust reduced order models (ROMs). The ROMs accept moderate variations of the material properties without pronounced loss in accuracy. This renders them an ideal candidate for the generation of quality data for feeding further data-hungry schemes such as Deep Material Networks, which require not too many but very expensive pre-calculations. The latter will be tuned such that they not only accept variable constitutive parameters, but the interpolation across the previously modeled, stochastic meso-structural geometries is targeted. Next, we will synthesize the methods from these three building blocks in order to run forward simulations in order to analyze the stochastic response of the structures and its correlation to meso-structural features. Finally, we envision a direct inverse model which recommends combinations of uncertain geometry and uncertain constitutive parameters. Thereby, the balancing of constitutive randomness and uncertain geometry in the design process will be facilitated: Is it worth to improve geometric accuracy? Should more homogeneous material properties be pursued? Which geometric features are criticial?