A Bayesian learning framework for fast prediction and uncertainty quantification of additively manufactured multi-material components

Abstract

Multi-material design in additive manufacturing relies on fast and accurate prediction of the physical response of mesostructured parts with arbitrary material distributions, which is extraordinarily challenging owing to the unknown parameters in constitutive modeling, manufacturing uncertainties, and high computational cost. Here, we employ an interdisciplinary framework to address these challenges by integrating experimentation, mechanical modeling, and statistical learning. Using advanced Bayesian learning and inference to optimally combine the simulation and experimental data, this framework enables (1) parameter calibration, (2) fast and accurate prediction of the physical response, and (3) uncertainty quantification of additively manufactured multi-material components. We demonstrate the framework based on a mechanical design problem involving three-point bending of multi-material beams. By training the Bayesian learning model with simulation and experimental data from selected multi-material designs, the beam deflection with an arbitrary mesostructure is shown to be accurately and rapidly predicted. Correlation of data sampling with the emulator uncertainty and discrepancy is demonstrated; this correlation can be used to identify regions with insufficient data sampling. The posterior distribution of each calibrated parameter is determined, revealing physical insights into the relative importance of these parameters in the mechanical design problem. By leveraging the advantages from both physically-based and data-driven approaches, the Bayesian learning framework allows for prediction and calibration using a somewhat small dataset, and therefore has great potential for widespread use in multi-material additive manufacturing applications.