Quantitative aspects of the rigidity of branching microstructures in shape memory alloys via h-measures

Theresa M. Simon

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Based on a geometrically linearized theory, we describe the partition into twins observed in microstructures of shape memory alloys undergoing cubic-to-tetragonal transformations in an ansatz-free way using H-measures, a tool of microlocal analysis to describe the direction of oscillations and concentration effects of weakly convergent sequences. As an application, we give a B2/31,∞-estimate for the characteristic functions of twins generated by finite energy sequences in the spirit of compactness for Γ-convergence. Heuristically, this suggests that the larger-scale interfaces, such as habit planes, can cluster on a set of Hausdorff-dimension 3-2/3. We provide evidence indicating that this fractional dimension is optimal. Furthermore, we get an essentially local lower bound for the blow-up behavior of the limiting energy density close to a habit plane.

Original languageEnglish (US)
Pages (from-to)4537-4567
Number of pages31
JournalSIAM Journal on Mathematical Analysis
Volume53
Issue number4
DOIs
StatePublished - 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Calculus of variations
  • H-measures
  • Linearized elasticity
  • Shape memory alloys

Fingerprint

Dive into the research topics of 'Quantitative aspects of the rigidity of branching microstructures in shape memory alloys via h-measures'. Together they form a unique fingerprint.

Cite this