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Estimating stress fluctuations in polycrystals using an improved maximum entropy method

Krause, Maximilian ORCID iD icon 1; Böhlke, Thomas ORCID iD icon 1
1 Institut für Technische Mechanik (ITM), Karlsruher Institut für Technologie (KIT)

Abstract:

The prediction of local field statistics from effective properties is an open problem in the field of micromechanics. Partial information on the local field statistics is accessible from homogenization assumptions. In particular, exact phase-wise second moments of stresses can be calculated analytically from the effective strain energy density. In recent years, full-field calculations have become efficient enough to sample large ensembles of microstructures in the plastic regime (e.g. Gehrig et. al [4]). In the present work, the maximum entropy method known from statistical thermodynamics is used to estimate first and second moments of local stresses from known eigenstrain distributions. The simple and refined formulations of the maximum entropy method proposed by Kreher and Pompe [9] are considered. While the simple method yields satisfactory results for a large amount of material classes (cf. Krause and Böhlke [7]), we prove that it does not respect the linearity of the eigenstrain problem. We further show that neither method corresponds to the exact second moments of stresses known from the effective strain energy density. By incorporating additional information, we find an improved maximum entropy method. ... mehr


Verlagsausgabe §
DOI: 10.5445/IR/1000155904
Veröffentlicht am 15.02.2023
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Technische Mechanik (ITM)
Publikationstyp Proceedingsbeitrag
Publikationsdatum 24.11.2022
Sprache Englisch
Identifikator ISBN: 9788412322286
ISSN: 2696-6999
KITopen-ID: 1000155904
Erschienen in ECCOMAS Congress 2022 - 8th European Congress on Computational Methods in Applied Sciences and Engineering
Veranstaltung 8th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2022), Oslo, Norwegen, 05.06.2022 – 09.06.2022
Verlag International Centre for Numerical Methods in Engineering (CIMNE)
Serie WCCM-ECCOMAS Congress
Schlagwörter Micromechanics, Maximum Entropy Method, Homogenization, Localization, Polycrystals
Nachgewiesen in Scopus
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