Kuhn, Charlotte ; Müller, Ralf ; Klassen, Markus ; Gross, Dietmar (2023)
Numerical homogenization of the Eshelby tensor at small strains.
In: Mathematics and Mechanics of Solids, 2020, 25 (7)
doi: 10.26083/tuprints-00016969
Artikel, Zweitveröffentlichung, Verlagsversion
 | Es ist eine neuere Version dieses Eintrags verfügbar. |
Kurzbeschreibung (Abstract)
Numerical homogenization methods, such as the FE² approach, are widely used to compute the effective physical properties of microstructured materials. Thereby, the macroscopic material law is replaced by the solution of a microscopic boundary value problem on a representative volume element in conjunction with appropriate averaging techniques. This concept can be extended to configurational or material quantities, like the Eshelby stress tensor, which are associated with configurational changes of continuum bodies. In this work, the focus is on the computation of the macroscopic Eshelby stress tensor within a small-strain setting. The macroscopic Eshelby stress tensor is defined as the volume average of its microscopic counterpart. On the microscale, the Eshelby stress tensor can be computed from quantities known from the solution of the physical microscopic boundary value problem. However, in contrast to the physical quantities of interest, i.e. stress and strain, the Eshelby stress tensor is sensitive to rigid body rotations of the representative volume element. In this work, it is demonstrated how this must be taken into account in the computation of the macroscopic Eshelby stress tensor. The theoretical findings are illustrated by a benchmark simulation and further simulation results indicate the microstructural influence on the macroscopic configurational forces.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2023 |
| Autor(en): | Kuhn, Charlotte ; Müller, Ralf ; Klassen, Markus ; Gross, Dietmar |
| Art des Eintrags: | Zweitveröffentlichung |
| Titel: | Numerical homogenization of the Eshelby tensor at small strains |
| Sprache: | Englisch |
| Publikationsjahr: | 28 November 2023 |
| Ort: | Darmstadt |
| Publikationsdatum der Erstveröffentlichung: | Juli 2020 |
| Ort der Erstveröffentlichung: | Thousand Oaks, California, USA |
| Verlag: | SAGE Publications |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Mathematics and Mechanics of Solids |
| Jahrgang/Volume einer Zeitschrift: | 25 |
| (Heft-)Nummer: | 7 |
| DOI: | 10.26083/tuprints-00016969 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/16969 |
| Zugehörige Links: | |
| Herkunft: | Zweitveröffentlichung DeepGreen |
| Kurzbeschreibung (Abstract): | Numerical homogenization methods, such as the FE² approach, are widely used to compute the effective physical properties of microstructured materials. Thereby, the macroscopic material law is replaced by the solution of a microscopic boundary value problem on a representative volume element in conjunction with appropriate averaging techniques. This concept can be extended to configurational or material quantities, like the Eshelby stress tensor, which are associated with configurational changes of continuum bodies. In this work, the focus is on the computation of the macroscopic Eshelby stress tensor within a small-strain setting. The macroscopic Eshelby stress tensor is defined as the volume average of its microscopic counterpart. On the microscale, the Eshelby stress tensor can be computed from quantities known from the solution of the physical microscopic boundary value problem. However, in contrast to the physical quantities of interest, i.e. stress and strain, the Eshelby stress tensor is sensitive to rigid body rotations of the representative volume element. In this work, it is demonstrated how this must be taken into account in the computation of the macroscopic Eshelby stress tensor. The theoretical findings are illustrated by a benchmark simulation and further simulation results indicate the microstructural influence on the macroscopic configurational forces. |
| Freie Schlagworte: | Numerical homogenization, Eshelby tensor, configurational forces, FE2, small strain |
| Status: | Verlagsversion |
| URN: | urn:nbn:de:tuda-tuprints-169697 |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 600 Technik, Medizin, angewandte Wissenschaften > 624 Ingenieurbau und Umwelttechnik |
| Fachbereich(e)/-gebiet(e): | 13 Fachbereich Bau- und Umweltingenieurwissenschaften 13 Fachbereich Bau- und Umweltingenieurwissenschaften > Fachgebiete der Mechanik 13 Fachbereich Bau- und Umweltingenieurwissenschaften > Fachgebiete der Mechanik > Fachgebiet Festkörpermechanik 13 Fachbereich Bau- und Umweltingenieurwissenschaften > Fachgebiete der Mechanik > Fachgebiet Kontinuumsmechanik |
| Hinterlegungsdatum: | 28 Nov 2023 10:39 |
| Letzte Änderung: | 29 Nov 2023 16:00 |
| PPN: | |
| Zugehörige Links: | |
| Export: | |
| Suche nach Titel in: | TUfind oder in Google |
Verfügbare Versionen dieses Eintrags
- Numerical homogenization of the Eshelby tensor at small strains. (deposited 28 Nov 2023 10:39) [Gegenwärtig angezeigt]
 |
Frage zum Eintrag |
Optionen (nur für Redakteure)
 |
Redaktionelle Details anzeigen |
Drucken
Impressum