An Information-Theoretic Multiscale Framework With Applications to Polycrystalline Materials

Abstract : The effect of diverse sources of uncertainties and the intrinsically multi-scale nature of physical systems poses a considerable challenge in their analysis. Such phenomena are particularly critical in material systems where the microstructural variability and randomness at different scales have a significant impact on the macroscopic behavior of the system. Toward this goal, during the period of this grant, we have developed a sophisticated though efficient and accurate multiscale stochastic framework for uncertainty quantification. A methodology is first developed to incorporate topological uncertainties in microstructures using a non-linear data-driven model reduction technique. This framework seamlessly allows for accessing the effects of microstructural variability on the reliability of macro-scale systems and provides an accurate stochastic input model into our stochastic system. Next, to solve the resulted stochastic partial different equations (SPDEs), an adaptive sparse grid collocation technique has been developed. In this framework, we construct the stochastic collocation points based on the function being represented, thus avoiding computational overhead. We further extended this framework to include the High Dimensional Model Representation (HDMR) technique in the stochastic space to represent the model output as a finite hierarchical correlated function expansion in terms of the stochastic inputs starting from lower-order to higher-order component functions. In this way, we can address the stochastic high dimensional problem for the first time in this area. We applied this framework for the design of general materials processes under uncertainty including the robust design of deformation processes of polycrystalline materials. We developed a unique data-driven strategy to encode the limited information on initial texture and grain distribution in deformation processes and represent it in a finite-dimensional framework.