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

Author: 

Kitavtsev, G
Lauteri, G
Luckhaus, S
Rueland, A

Publication Date: 

April 2019

Journal: 

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

Last Updated: 

2019-05-09T16:09:33.293+01:00

Issue: 

1

Volume: 

232

DOI: 

10.1007/s00205-018-1327-0

page: 

531-555

abstract: 

© 2018, The Author(s). 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.

Symplectic id: 

923712

Download URL: 

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article