Multiscale and Multidimensional Uncertainty Quantification in Integrated Computational Materials Engineering


Integrated Computational Materials Engineering hinges on engineering microstructural features into the materials design process where the overarching goal is to search for materials with superior structure-level performance while considering the geometrical and manufacturing constraints. Over the past few decades, computational materials science and mechanics have come a long way to achieve this goal by replacing costly experiments that rely on trial-and-error with multiscale simulations. However, to arrive at predictions that match with the observed stochasticity in materials, it is of utmost importance to systematically account for the inherent uncertainty of the physical system in multiscale simulations. Inherent uncertainties are inevitably introduced in materials’ behavior starting from the design and constituent selection stages, through the manufacturing processes, and finally during operation. Computer simulations bear additional uncertainty sources that stem from, e.g., calibration, lack of knowledge on the underlying physics, or limited computational resources. Quantification of these uncertainties is significantly challenging since they are multi-dimensional, spread across different length-scales, spatially correlated, and embody different characteristics (e.g., topological vs. property-related).


In this talk, we address these challenges by presenting a non-intrusive computational approach for multiscale and multidimensional uncertainty quantification. We introduce the top-down sampling method that allows to model non-stationary and continuous (but not differentiable) spatial variations of uncertainty sources by creating nested random fields. We employ multi-response Gaussian random processes in top-down sampling and leverage sensitivity analyses and supervised learning to address the considerable computational costs of multiscale simulations. We apply our approach to quantify the uncertainty in the multiscale simulation of a cured woven composite. Additionally, our approach can be seamlessly integrated with image-based microstructure characterization and reconstruction techniques to leverage imaging data. We demonstrate this on unidirectional carbon fiber composites where experimental images are employed to develop a segmented regression approach for quantifying fiber waviness in the transverse plane. The nonstationarity and inhomogeneity of the fiber distribution in the images is modeled with a tree-structured nonhomogeneous Poisson point process. The broader impact is to pin down the main sources of uncertainty and correspondingly reduce the production costs by guiding the manufacturing and quality control processes.


Predictions from computer simulations are more valuable once they are validated and calibrated against some experimental data. To this end, we introduce a physics-informed modular Bayesian approach where the lack of experimental and simulation resources is addressed by enforcing certain physical constraints on the functional forms of the simulator and its potential discrepancies in the Bayesian analyses. The developed approach can estimate the calibration parameters of a constitutive law while considering its potential discrepancies with the true physical system. The corrected constitutive law is subsequently used to model the multiscale preforming process in manufacturing carbon composites. The same model validation and uncertainty quantification approach can be applied to ICME of other multiscale materials systems.