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

Abstract

In this note we combine the "spin-argument" from [KLR15] and the $n$-dimensional incompatible, one-well rigidity result from [LL16], 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.

19 pages, 2 figures

References in corpus (2)

• Interfaces, modulated phases and textures in lattice systems
• An Energy Estimate for Dislocation Configurations and the Emergence of Cosserat-Type Structures in Metal Plasticity

Cited by in corpus (1)

• On the Scaling of the Cubic-to-Tetragonal Phase Transformation with Displacement Boundary Conditions