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Most modern physics-based multiscale materials modeling and simulation tools aim to take into account the important details of the material internal structure at multiple length scales. However, they are extremely computationally expensive. In recent years, our group formulated a novel data science enabled framework for effective scale-bridging that is central to practical multiscaling. A salient feature of this new approach is its ability to capture heterogeneity of fields of interest at different length scales. In this approach, the computations at the mesoscale are handled using a novel data science approach called materials knowledge systems (MKS). The MKS approach has enjoyed tremendous success in building highly accurate and computationally efficient metamodels for localization (i.e., mesoscale spatial distribution of a macroscale imposed field such as stress or strain rate) in simulating a number of different multiscale materials phenomena. MKS derives its accuracy from the fact that it is calibrated to results from previously established numerical models for the phenomena of interest, while its computational efficiency comes from the use of fast Fourier transforms.
MKS approach is also utilized to capture and communicate critical information regarding the evolution of material structure in multiscale simulations. It was previously applied successfully for capturing mainly the microstructure-property linkages in spatial multiscale simulations. The approach is generalized by introducing different basis functions, and their potential benefits in establishing the desired process-structure-property (PSP) linkages are explored. These new developments have already been demonstrated for Cahn-Hilliard simulations, where structure evolution was predicted three orders of magnitude faster than an optimized numerical integration algorithm.
MKS localization framework provides an alternate method to learn the underlying embedded physics in a numerical model expressed through Green’s function based influence kernels rather than differential equations, and potentially offers significant computational advantages in problems where numerical integration schemes are challenging to optimize. With this extension, our research has established a comprehensive framework for capturing PSP linkages for multiscale materials modeling and simulations in both space and time.