Calibrated localization relationships for elastic response of polycrystalline aggregates

Machine learning approaches for elastic localization linkages in high-contrast composite materials

“…Further details regarding these periodic boundary conditions and the approaches described above can be found in our prior work [15]. For the present study, following protocols used in prior studies, each MVE was selected to consist of 21 × 21 × 21 = 9261 voxels [15,22,33]. Each element in the MVE is assigned one of the two possible phases depicted as black and white in Fig.…”

“…Following the symbolic definitions in [15][16][17][18][19]22], we let the microstructure variables m 0 s and m 1 s denote the volume fraction of each local state in each voxel of the composite MVE, where 0 < s ≤ S indexes the voxels; S = 9261 is the total number of voxels in an MVE. Since m 1 s + m 0 s = 1 and we employ eigenmicrostructures (each voxel is assigned exclusively to one of the two phases allowed) in the present case study, we further simplify the notation and use m s to simply denote m 1 s in some of the case studies presented here.…”

“…Thus, the errors are expected to be considerably lower with lower contrasts. The error measures and results for lower contrast materials systems have been reported in prior work [15,19,22,33]. More specifically, our goal here is to mine localization linkages from an accumulated set of observations and then use the extracted models to predict the response in new, not yet analyzed, structures.…”

“…The higher value knowledge extracted using these tools can be used to dramatically accelerate material development efforts for a range of advanced technologies. One of the central tasks in the analyses of materials data is the identification and extraction of robust and reliable structure-property relationships [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33].…”

Context Aware Machine Learning Approaches for Modeling Elastic Localization in Three-Dimensional Composite Microstructures

“…Historically, the multiscale materials modeling efforts have addressed either homogenization (communication of information from the lower length scale to the higher length scale) [30][31][32][33] or localization (communication of information from the higher length scale to the lower length scale) [8,13,14,[34][35][36]. Although both homogenization and localization have been studied extensively in literature using physically based approaches [31][32][33]37], recent work has identified the tremendous benefits of fusing these approaches with data-driven approaches [8,13,14,30,[34][35][36]. However, most of the prior effort has only addressed a limited number of the multiscale features.…”