Khalaquzzaman, Md. ; Xu, Bai-Xiang ; Müller, Ralf (2012)
Computational homogenization of materials with small deformation to determine configurational forces.
In: PAMM — Proceedings in Applied Mathematics and Mechanics, 12 (1)
doi: 10.1002/pamm.201210200
Artikel, Bibliographie
Kurzbeschreibung (Abstract)
n this work the mechanical boundary condition for the micro problem in a two-scaled homogenization using a FE2 approach is discussed. The strain tensor is often used in the literature for small deformation problem to determine the boundary conditions for the boundary value problem on the micro level. This strain tensor based boundary condition gives consistent homogenized mechanical quantities, e.g. stress tensor and elasticity tensor, but the present work points out that it leads to unphysical homogenized configurational forces. Instead, we propose a displacement gradient based boundary condition for the micro problem. Results show that the displacement gradient based boundary condition can give not only the consistent homogenized mechanical quantities but also the appropriate homogenized configurational forces. The interpretation of the displacement gradient based boundary condition is discussed.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2012 |
| Autor(en): | Khalaquzzaman, Md. ; Xu, Bai-Xiang ; Müller, Ralf |
| Art des Eintrags: | Bibliographie |
| Titel: | Computational homogenization of materials with small deformation to determine configurational forces |
| Sprache: | Englisch |
| Publikationsjahr: | Dezember 2012 |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | PAMM — Proceedings in Applied Mathematics and Mechanics |
| Jahrgang/Volume einer Zeitschrift: | 12 |
| (Heft-)Nummer: | 1 |
| DOI: | 10.1002/pamm.201210200 |
| URL / URN: | https://onlinelibrary.wiley.com/doi/pdf/10.1002/pamm.2012102... |
| Kurzbeschreibung (Abstract): | n this work the mechanical boundary condition for the micro problem in a two-scaled homogenization using a FE2 approach is discussed. The strain tensor is often used in the literature for small deformation problem to determine the boundary conditions for the boundary value problem on the micro level. This strain tensor based boundary condition gives consistent homogenized mechanical quantities, e.g. stress tensor and elasticity tensor, but the present work points out that it leads to unphysical homogenized configurational forces. Instead, we propose a displacement gradient based boundary condition for the micro problem. Results show that the displacement gradient based boundary condition can give not only the consistent homogenized mechanical quantities but also the appropriate homogenized configurational forces. The interpretation of the displacement gradient based boundary condition is discussed. |
| Fachbereich(e)/-gebiet(e): | 11 Fachbereich Material- und Geowissenschaften 11 Fachbereich Material- und Geowissenschaften > Materialwissenschaft 11 Fachbereich Material- und Geowissenschaften > Materialwissenschaft > Fachgebiet Mechanik Funktionaler Materialien 13 Fachbereich Bau- und Umweltingenieurwissenschaften 13 Fachbereich Bau- und Umweltingenieurwissenschaften > Fachgebiete der Mechanik 13 Fachbereich Bau- und Umweltingenieurwissenschaften > Fachgebiete der Mechanik > Fachgebiet Kontinuumsmechanik Exzellenzinitiative Exzellenzinitiative > Graduiertenschulen Exzellenzinitiative > Graduiertenschulen > Graduate School of Computational Engineering (CE) Zentrale Einrichtungen |
| Hinterlegungsdatum: | 18 Apr 2013 07:35 |
| Letzte Änderung: | 26 Jan 2024 09:21 |
| PPN: | |
| Sponsoren: | The authors acknowledge financial support of German Research Foundation (DFG) in the framework of Graduate Program GRK-814 and the Center for Mathematical and Computational Modelling (CM) 2 at TU Kaiserslautern |
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