Calibrated localization relationships for elastic polycrystalline aggregates
Yabansu, Yuksel C.
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Multiscale modeling of material systems demands novel solution strategies to simulating physical phenomena that occur in a hierarchy of length scales. Majority of the current approaches involve one way coupling such that the information is transferred from a lower length scale to a higher length scale. To enable bi-directional scale-bridging, a new data-driven framework called Materials Knowledge System (MKS) has been developed recently. The remarkable advantages of MKS in establishing computationally efficient localization linkages (e.g., spatial distribution of a field in lower length scale for an imposed loading condition in higher length scale) have been demonstrated in prior work. In prior work, the viability and computational advantages of the MKS approach were demonstrated in a number of case studies involving multiphase composites, where the local material state in each spatial bin of the volume element was permitted to be any one of a limited number of material phases (i.e., restricted to a set of discrete local states of the material). As a major extension, the MKS framework has been extended for polycrystalline aggregates which need to incorporate crystal lattice orientation as a continuous local state. Another important extension of the MKS approach that permits calibration of the influence kernels of the localization linkages for an entire class of low to moderate contrast material systems will also be presented. This major extension of the MKS framework for elastic deformation of polycrystals is achieved by employing compact Fourier representations of functions defined in the crystal orientation space. The viability of this new formulation will be presented for several case studies involving single and multi-phase polycrystals.