AN INFORMATION-THEORETIC MULTISCALE FRAMEWORK WITH APPLICATIONS TO POLYCRYSTALLINE MATERIALS AFOSR GRANT NUMBER FA9550-07-1-0139 Prof

The effect of diverse sources of uncertainties and the intrinsically multi-scale nature of real-world physical systems poses a considerable challenge to analyze such systems. Such phenomena are particularly critical in material systems wherein microstructural variability and randomness at lower scales have a significant impact on the behavior of the system. Towards this goal, some of our accomplishments over the last year include the development of an adaptive sparse grid collocation technique for multiscale systems, development of a stochastic variational multiscale framework and developing tools for robust design for deformation processes. In our adaptive hierarchical sparse-grid framework, we developed a technique that constructs the stochastic collocation points based on the function being represented, thus avoiding the computational overhead associated with superfluous collocation points. We derived a multiscale stochastic framework that can resolve the stochastic and multiscale components of a system simultaneously. A stochastic analogue of the mixed multiscale finite element technique using concepts from adaptive sparse grid collocation was employed for the same. We have also developed a methodology 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. In addition, we recently applied the adaptive sparse-grid collocation scheme for the design of general processes under uncertainty including the robust design of deformation processes of polycrystalline materials.