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Generated microstructure based on an experimentally
determined fiber length distribution.
​Modern Short Fiber Reinforced Polymer (SFRP) components are produced using a variety of manufacturing processes that have a large impact on the final material properties. In order to be able to predict the final material properties via FFT-based computational homogenization techniques, a digital twin of the underlying microstructure of the components is required. Digital imaging techniques such as µ-CT are expensive and time consuming. Therefore, we develop numerical methods to generate realistic digital microstructures, based on the prescribed fiber volume fraction, fiber orientations, and fiber lengths. In this context, we have developed special techniques that are able to generate microstructures with an arbitrary prescribed fiber length distribution.

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Strain field (above) and slice of the strain field (below) due to
a non-zero Dirichlet boundary condition in the shape of the
UDE signet on a cubic microstructure with a spherical inclusion.
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​Computational homogenization methods based on the FFT permit to determine the effective mechanical properties of microstructured materials in a fast and resource-efficient way. By operating on microstructures given on a regular grid and harnessing the efficiency of existing FFT implementations, a considerable performance advantage over conventional interface-conforming Finite Element (FE)-based methods is achieved. Until recently, the comparison and validation with either FE-based results or experimental data were hampered by the FFT-based method’s inherent application of periodic boundary conditions on the domain faces. Often, non-periodic boundary conditions are required to validate real-world experiments. In this project, we develop approaches to apply non-periodic boundary conditions for FFT-based computational homogenization of mechanical problems by employing discrete sine and cosine transforms while retaining the advantages of FFT-based methods regarding speed and efficiency.
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