Kuhn, Charlotte ; Müller, Ralf (2011)
On an Energetic Interpretation of a Phase Field Model for Fracture.
In: PAMM, 11 (1)
doi: 10.1002/pamm.201110071
Artikel, Bibliographie
Kurzbeschreibung (Abstract)
In the pioneering work by Griffith, it is assumed that a crack propagates, if this is energetically favorable. However, this original formulation requires a pre-existing initial crack. In order to bypass this deficiency of classical Griffith theory, Francfort and Marigo advocate a global variational criterion, where the total energy is minimized with respect to any admissible displacement field and crack set. Bourdin's regularized approximation of this variational formulation makes use of a continuous scalar field to indicate cracks. Based on this regularization a phase field fracture model is formulated. The crack field is assumed to follow a Ginzburg-Landau type evolution equation, and cracking is addressed as a phase transition problem. The coupled problem of mechanical balance equations and the evolution equation is solved using the finite element method combined with an implicit time integration scheme. The numerical solution naturally yields the crack evolution including crack propagation, kinking, branching and initiation without any additional criteria. In this work we study the driving mechanisms behind the crack evolution in the phase field fracture model and compare to the purely energetic considerations of the underlying variational formulation. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2011 |
| Autor(en): | Kuhn, Charlotte ; Müller, Ralf |
| Art des Eintrags: | Bibliographie |
| Titel: | On an Energetic Interpretation of a Phase Field Model for Fracture |
| Sprache: | Englisch |
| Publikationsjahr: | 9 Dezember 2011 |
| Verlag: | Wiley |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | PAMM |
| Jahrgang/Volume einer Zeitschrift: | 11 |
| (Heft-)Nummer: | 1 |
| DOI: | 10.1002/pamm.201110071 |
| URL / URN: | https://onlinelibrary.wiley.com/doi/abs/10.1002/pamm.2011100... |
| Kurzbeschreibung (Abstract): | In the pioneering work by Griffith, it is assumed that a crack propagates, if this is energetically favorable. However, this original formulation requires a pre-existing initial crack. In order to bypass this deficiency of classical Griffith theory, Francfort and Marigo advocate a global variational criterion, where the total energy is minimized with respect to any admissible displacement field and crack set. Bourdin's regularized approximation of this variational formulation makes use of a continuous scalar field to indicate cracks. Based on this regularization a phase field fracture model is formulated. The crack field is assumed to follow a Ginzburg-Landau type evolution equation, and cracking is addressed as a phase transition problem. The coupled problem of mechanical balance equations and the evolution equation is solved using the finite element method combined with an implicit time integration scheme. The numerical solution naturally yields the crack evolution including crack propagation, kinking, branching and initiation without any additional criteria. In this work we study the driving mechanisms behind the crack evolution in the phase field fracture model and compare to the purely energetic considerations of the underlying variational formulation. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) |
| 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 Kontinuumsmechanik |
| Hinterlegungsdatum: | 04 Mai 2022 09:14 |
| Letzte Änderung: | 04 Mai 2022 09:14 |
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