Advanced Computational Techniques for Materials-by-Design

Abstract : Modeling of uncertainty propagation in multi-scale models of deformation is extremely complex considering the nonlinear coupled phenomena that need to be accounted for. The ongoing work addresses key mathematical and computational issues related to robust control of deformation processes. Our research accomplishments for this year include development of new mathematical models based on spectral polynomial chaos, support space, and entropy maximization techniques for modeling sources of uncertainties in material deformation processes. These models, in conjunction with multi-scale models, allow simulations of the effect of microstructural variability on the reliability of macroscale systems. We have developed the first stochastic variational multi-scale simulator with explicit sub-grid modeling, and a robust deformation process simulator for simulating uncertainties in metal forming processes. The non-intrusive stochastic Galerkin method developed as a part of the deformation simulator provides highly accurate estimates of the statistical quantities of interest within a fraction of time required using existing Monte-Carlo methods, and with minimal modification of existing deterministic software. The technique has also been applied to enable stochastic optimization of deformation processes. Finally, an information theoretic framework to capture microstructural uncertainties and its effect on macro-scale properties is summarized.