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Characterizing digital microstructures by the Minkowski‐based quadratic normal tensor

Ernesti, Felix 1; Schneider, Matti 1; Winter, Steffen 2; Hug, Daniel ORCID iD icon 2; Last, Günter 2; Böhlke, Thomas ORCID iD icon 1
1 Institut für Technische Mechanik (ITM), Karlsruher Institut für Technologie (KIT)
2 Institut für Stochastik (STOCH), Karlsruher Institut für Technologie (KIT)

Abstract:

For material modeling of microstructured media, an accurate characterization of the underlying microstructure is indispensable. Mathematically speaking, the overall goal of microstructure characterization is to find simple functionals which describe the geometric shape as well as the composition of the microstructures under consideration and enable distinguishing microstructures with distinct effective material behavior. For this purpose, we propose using Minkowski tensors, in general, and the quadratic normal tensor, in particular, and introduce a computational algorithm applicable to voxel-based microstructure representations. Rooted in the mathematical field of integral geometry, Minkowski tensors associate a tensor to rather general geometric shapes, which make them suitable for a wide range of microstructured material classes. Furthermore, they satisfy additivity and continuity properties, which makes them suitable and robust for large-scale applications. We present a modular algorithm for computing the quadratic normal tensor of digital microstructures. We demonstrate multigrid convergence for selected numerical examples and apply our approach to a variety of microstructures. ... mehr


Verlagsausgabe §
DOI: 10.5445/IR/1000149484
Veröffentlicht am 10.08.2022
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Institut für Technische Mechanik (ITM)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2022
Sprache Englisch
Identifikator ISSN: 0170-4214, 1099-1476
KITopen-ID: 1000149484
Erschienen in Mathematical Methods in the Applied Sciences
Verlag John Wiley and Sons
Band 46
Heft 1
Seiten 961-985
Vorab online veröffentlicht am 25.07.2022
Nachgewiesen in Scopus
Web of Science
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