Abstract
In this thesis, a computational scheme was developed to generate thousands of microstructure realizations of unidirectional composites with random fiber distributions employed by the homogenization theory called FVDAM. Once the microstructure was realized using randomly distributed fiber centers, it was then discretized into equally dimensioned subvolumes, and the material assignment matrix was created for input into FVDAM simulation. Subsequently, the FVDAM homogenization theory was incorporated into a python-driven interface that enabled generation of thousands of elastic-plastic stress-strain curves for unidirectional metal matrix composites with random fiber distributions. The generated microstructure realizations, the corresponding homogenized elastic moduli and stress-strain responses were then employed in ANN and CNN architectures that were designed and optimized for predictive purposes.
The calculated homogenized moduli and stress-strain responses under six fundamental loading modes were first correlated with the microstructural realizations to understand the effect of random fiber distributions on the response in the elastic and elastic-plastic regions. Whereas the effect of fiber randomness on the homogenized moduli is small, it is much larger on the elastic-plastic response, but also dependent on the loading direction relative to the fiber orientation. As expected, and confirmed by simulations herein, the microstructural randomness has virtually no effect on the response by uniaxial loading along the fiber direction due to the constraint of the fibers that controls the plastic strain evolution. Large microstructure effects are seen under normal loading transverse to the fiber direction, which become somewhat smaller under transverse shear and smaller still under axial shear.
Subsequently, deep ANN and CNN architectures were designed and optimized to predict both the homogenized elastic moduli and direction-dependent elastic-plastic stress-strain responses of microstructural realizations representative of random fiber composites. Whereas the input to the ANN model consisted of fiber placement locations, the CNN model employed full-field microstructural images discretized into subvolumes or pixels. Nineteen hundred and fifty microstructural realizations were sufficient for training, testing and validation, which produced very good prediction of the homogenized stress-strain responses of the remaining fifty realizations by both ANN and CNN algorithms. In contrast, 20,000 realizations were required for the prediction of the 13 homogenized elastic moduli based on the CNN algorithm due to the small effect of random fiber microstructures. Nonetheless, the CNN algorithm successfully captured the very small moduli indicative of monoclinic behavior several orders of magnitude smaller than the moduli characteristic of orthotropic response. By contrast, the ANN algorithm did not perform well due to the input data type and the size of the training data set, likely because the small differences in the homogenized moduli produced by fiber placement variations required significantly larger number of features and/or data for accurate prediction.
The algorithms and generated results reported in the thesis are important in developing accurate ML-based computational models for implementation in multi-scale analyses of large-scale composite structures. Perhaps most significantly, the execution times required to predict the homogenized elastic-plastic response of random fiber composites based on the ANN/CNN algorithms are several orders of magnitude smaller that the full-scale calculations based on the FVDAM homogenization theory, enabling multi-scale analysis of composite structures.
