Study of an alternative phase field model for low interfacial energy in elastic solids
In 2005, the hybrid model was published by Prof. H.-D. Alber and Prof. P. Zhu as an alternative to the Allen-Cahn model for the description of phase field transformations. With low interfacial energy, it is more efficient, since the resolution of the diffuse interface is numerically broader for the...
Αποθηκεύτηκε σε:
| Κύριος συγγραφέας: | |
|---|---|
| Μορφή: | Online |
| Γλώσσα: | Αγγλικά |
| Έκδοση: |
Logos Verlag Berlin
2022
|
| Θέματα: | |
| Διαθέσιμο Online: | OCN: 1296711993 |
| Ετικέτες: |
Δεν υπάρχουν, Καταχωρήστε ετικέτα πρώτοι!
|
| _version_ | 1869514175275859968 |
|---|---|
| author | Böttcher, Anke |
| author_browse | Böttcher, Anke |
| author_facet | Böttcher, Anke |
| author_sort | Böttcher, Anke |
| collection | Directory of Open Access Books |
| description | In 2005, the hybrid model was published by Prof. H.-D. Alber and Prof. P. Zhu as an alternative to the Allen-Cahn model for the description of phase field transformations. With low interfacial energy, it is more efficient, since the resolution of the diffuse interface is numerically broader for the same solution accuracy and allows coarser meshing. The solutions of both models are associated with energy minimisation and in this work the error terms introduced in the earlier publications are discussed and documented using one and two dimensional numerical simulations. In the last part of this book, phase field problems, initially not coupled with material equations, are combined with linear elasticity and, after simple introductory examples, a growing martensitic inclusion is simulated and compared with literature data. In addition to the confirmed numerical advantage, another phenomenon not previously described in the literature is found: with the hybrid model, in contrast to the examples calculated with the Allen-Cahn model, an inclusion driven mainly by curvature energy does not disappear completely. The opposite problem prevents inclusions from growing from very small initial configurations, but this fact can be remedied by a very finely chosen diffuse interface width and by analysing and adjusting the terms that generate the modelling errors. The last example shows that the hybrid model can be used with numerical advantages despite the above mentioned peculiarities. |
| format | Online |
| id | doab-20.500.12854ir-77437 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2022 |
| publishDateRange | 2022 |
| publishDateSort | 2022 |
| publisher | Logos Verlag Berlin |
| publisherStr | Logos Verlag Berlin |
| record_format | ojs |
| spelling | doab-20.500.12854ir-774372025-07-31T11:19:31Z Study of an alternative phase field model for low interfacial energy in elastic solids Böttcher, Anke Science Chemistry Mathematics Science Physics thema EDItEUR::P Mathematics and Science::PN Chemistry thema EDItEUR::P Mathematics and Science::PB Mathematics thema EDItEUR::P Mathematics and Science::PH Physics In 2005, the hybrid model was published by Prof. H.-D. Alber and Prof. P. Zhu as an alternative to the Allen-Cahn model for the description of phase field transformations. With low interfacial energy, it is more efficient, since the resolution of the diffuse interface is numerically broader for the same solution accuracy and allows coarser meshing. The solutions of both models are associated with energy minimisation and in this work the error terms introduced in the earlier publications are discussed and documented using one and two dimensional numerical simulations. In the last part of this book, phase field problems, initially not coupled with material equations, are combined with linear elasticity and, after simple introductory examples, a growing martensitic inclusion is simulated and compared with literature data. In addition to the confirmed numerical advantage, another phenomenon not previously described in the literature is found: with the hybrid model, in contrast to the examples calculated with the Allen-Cahn model, an inclusion driven mainly by curvature energy does not disappear completely. The opposite problem prevents inclusions from growing from very small initial configurations, but this fact can be remedied by a very finely chosen diffuse interface width and by analysing and adjusting the terms that generate the modelling errors. The last example shows that the hybrid model can be used with numerical advantages despite the above mentioned peculiarities. 2022-01-21T04:02:37Z 2022-01-21T04:02:37Z 2022-01-20T05:31:35Z 2021 book OCN: 1296711993 https://library.oapen.org/handle/20.500.12657/52509 9783832553371 9783832553371 https://directory.doabooks.org/handle/20.500.12854/77437 eng open access image/jpeg image/jpeg image/jpeg image/jpeg image/jpeg n/a n/a n/a n/a n/a https://library.oapen.org/bitstream/20.500.12657/52509/1/external_content.pdf https://library.oapen.org/bitstream/20.500.12657/52509/1/external_content.pdf https://library.oapen.org/bitstream/20.500.12657/52509/1/external_content.pdf https://library.oapen.org/bitstream/20.500.12657/52509/1/external_content.pdf https://library.oapen.org/bitstream/20.500.12657/52509/1/external_content.pdf Logos Verlag Berlin Logos Verlag Berlin https://doi.org/10.30819/5337 https://doi.org/10.30819/5337 04b263a1-7fba-4491-9eae-1c394ac42fc3 9783832553371 9783832553371 Knowledge Unlatched (KU) KU Open Services Logos Verlag Berlin open access |
| spellingShingle | Science Chemistry Mathematics Science Physics thema EDItEUR::P Mathematics and Science::PN Chemistry thema EDItEUR::P Mathematics and Science::PB Mathematics thema EDItEUR::P Mathematics and Science::PH Physics Böttcher, Anke Study of an alternative phase field model for low interfacial energy in elastic solids |
| title | Study of an alternative phase field model for low interfacial energy in elastic solids |
| title_full | Study of an alternative phase field model for low interfacial energy in elastic solids |
| title_fullStr | Study of an alternative phase field model for low interfacial energy in elastic solids |
| title_full_unstemmed | Study of an alternative phase field model for low interfacial energy in elastic solids |
| title_short | Study of an alternative phase field model for low interfacial energy in elastic solids |
| title_sort | study of an alternative phase field model for low interfacial energy in elastic solids |
| topic | Science Chemistry Mathematics Science Physics thema EDItEUR::P Mathematics and Science::PN Chemistry thema EDItEUR::P Mathematics and Science::PB Mathematics thema EDItEUR::P Mathematics and Science::PH Physics |
| topic_facet | Science Chemistry Mathematics Science Physics thema EDItEUR::P Mathematics and Science::PN Chemistry thema EDItEUR::P Mathematics and Science::PB Mathematics thema EDItEUR::P Mathematics and Science::PH Physics |
| url | OCN: 1296711993 |
| work_keys_str_mv | AT bottcheranke studyofanalternativephasefieldmodelforlowinterfacialenergyinelasticsolids |