A Compactness and Structure Result for a Discrete Multi-well Problem with SO(n) Symmetry in Arbitrary Dimension


Kitavtsev G., Lauteri G., Luckhaus S., Rüland A.

Archive for Rational Mechanics and Analysis, cilt.232, sa.1, ss.531-555, 2019 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 232 Sayı: 1
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1007/s00205-018-1327-0
  • Dergi Adı: Archive for Rational Mechanics and Analysis
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.531-555
  • Orta Doğu Teknik Üniversitesi Kuzey Kıbrıs Kampüsü Adresli: Hayır

Özet

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.