Uncertainty quantification of local elastic properties in additively manufactured materials for topology optimization applications using machine learning

The layering approach utilized in fused filament fabrication (FFF) enables the creation of complex designs generated by topology optimization. However, defects associated with the layer-by-layer process, often observed along the thin fusion regions, introduce considerable random variability to the local elastic modulus of the print. The elastic modulus along the fusion layers connecting bulk materials differs from that of the bulk areas. Accurate quantitative measurements of variations in both areas are essential to achieve robust optimized designs. In this study, we aim to quantify the parameters of the random distributions given the surface strain field of the print measured by digital image correlation (DIC). Two statistical properties, mean and standard deviation, are considered sufficient to characterize the stochastic elastic modulus fields in each region. We developed an efficient neural network model to estimate spatial variations in the local elastic modulus within both bulk and fusion layers. We trained the model on a dataset of synthetic strain fields with known elastic modulus distributions. The model performs well in correlating the elastic modulus with the input strain, provided that the standard deviation remains below 60% of the mean of the random field. The predictive accuracy of the model on testing data, measured by the R² score, is 0.99 and 0.95 for the mean and standard deviation in the fusion material. The scores for the bulk material are 0.97 each. We then applied the trained model to predict the elastic modulus distribution of an FFF-printed material at a print speed of 30 mm/s and an extrusion temperature of 220 °C, based on its DIC-measured surface strain data. The model predicts a mean and standard deviation of 1.2 GPa and 1 GPa for the bulk material, and 400 MPa and 430 MPa for the fusion region. Validation of these predictions confirms the reliability and credibility of this approach in quantifying uncertainty in the local properties of the prints.