Co-authors​ :

 Nils MEYER (GERMANY), Stefan PANZER (GERMANY) 

Injection molding and compression molding are cost-effective processes for manufacturing discontinuous fiber reinforced polymer composite parts with complex geometries. The resulting properties of such parts depend on local fiber orientations which can be either computed with process simulations [1], determined experimentally via X-ray micro computed tomography [2], or image analysis of micrographs [3]. However, process simulations are time consuming, require extensive calibration of material models and feature inaccuracies due to modeling assumptions. Micro computed tomography scans are also time consuming, require expensive equipment and are difficult to perform if the phase contrast is low, e.g. in carbon fiber polymer composites. Image analysis of micrographs requires labor-intensive (destructive) specimen preparation, uses assumptions about the cross section of fibers and is limited to two-dimensional images.
Therefore, our approach attempts to solve the inverse problem: Given the deformation field of a part measured via digital image correlation (DIC), we determine the local orientations leading to that deformation. We model the structural deformation of the part with a differentiable finite element solver [4] and mean field homogenization. Subsequently, we compute the error to the DIC measurement and minimize that error with respect to the input orientations. The gradients for optimization of the finite element model are computed efficiently using automatic differentiation with PyTorch through the entire model. The method is validated and discussed using different tensile specimens, but it can be extended to arbitrary parts with defined load cases and available DIC data.