A compactness and structure result for a discrete multi-well problem with SO(n) symmetry in arbitrary dimension
In this note we combine the “spin-argument” from Kitavtsev et al. (Proc R Soc Edinb Sect A Mater 147(5):1041-1089, 2017) and the n-dimensional incompatible, one-well rigidity result from Lauteri and Luckhaus (An energy estimate for dislocation configurations and the emergence of Cosserat-type struct...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article (Journal) |
| Language: | English |
| Published: |
2019
|
| In: |
Archive for rational mechanics and analysis
Year: 2018, Volume: 232, Issue: 1, Pages: 531-555 |
| ISSN: | 1432-0673 |
| DOI: | 10.1007/s00205-018-1327-0 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1007/s00205-018-1327-0
|
| Author Notes: | Georgy Kitavtsev, Gianluca Lauteri, Stephan Luckhaus & Angkana Rüland |
| Summary: | In this note we combine the “spin-argument” from Kitavtsev et al. (Proc R Soc Edinb Sect A Mater 147(5):1041-1089, 2017) and the n-dimensional incompatible, one-well rigidity result from Lauteri and Luckhaus (An energy estimate for dislocation configurations and the emergence of Cosserat-type structures in metal plasticity, 2016), in order to infer a new proof for the compactness of discrete multi-well energies associated with the modelling of surface energies in certain phase transitions. Mathematically, a main novelty here is the reduction of the problem to an incompatible one-well problem. The presented argument is very robust and applies to a number of different physically interesting models, including for instance phase transformations in shape-memory materials but also anti-ferromagnetic transformations or related transitions with an “internal” microstructure on smaller scales. |
|---|---|
| Item Description: | Published: 20 October 2018 Gesehen am 19.05.2021 |
| Physical Description: | Online Resource |
| ISSN: | 1432-0673 |
| DOI: | 10.1007/s00205-018-1327-0 |