Multiscale modeling based on a novel combination of direct data-driven methods with Fourier transform-based microstructure simulation

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It is largely undisputed that multi-scale calculations of materials with complex microstructures can provide valuable information for their use in practical applications. However, the use of suitable computational methods in practice is hampered by several challenges: (a) the excessively long computation times, (b) the insufficient identification of parameters at the microstructure level, caused, among other things, by uncertainties related to varying microstructures, and (c) different scales. The aim of the present project is to significantly reduce these disadvantages by a novel combination and further development of data-driven methods for inelastic material modeling with efficient microstructure simulations based on fast Fourier transforms (FFT). The so-called direct data-driven (DD) method is to be used, in which the data are transferred into a finite element (FE) model without further interpolation. In case of missing data, these are generated directly using FFT-based microstructure simulation. This results in a two-scale DD-FFT-based algorithm, where the DD method is incorporated into an FE model at the macro level. The present application intends to (1) further develop the direct data-driven methodology for inelastic materials considering uncertainties, (2) adaptively acquire data with efficient FFT-based simulations for complex inelastic materials at the microstructure level, (3) further develop model reduction techniques for particularly efficient FFT-based simulation, and (4) develop strategies on how to optimally combine data acquisition and data-driven simulation. Thus, an efficient two-scale data-driven computation should be enabled, which can also account for uncertainties in the microstructure. For adaptive data acquisition, the microstructure is best captured with FFT-based simulation, since the image-processing nature of the method allows varying microstructures to be studied in a straightforward manner.