Surface Energies Arising in Microscopic Modeling of Martensitic Transformations in Shape-Memory Alloys

Georgy Kitavtsev, Stephan Luckhaus, Angkana Rueland

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

Abstract

In this study we construct and analyze a two-well Hamiltonian on a 2D atomic lattice.The two wells of the Hamiltonian are prescribed by two rank-one connected martensitic twins, respectively. By constraining the deformed configurations to special 1D atomic chains with position-dependent elongation vectors for the vertical direction, we show that the structure of ground states under appropriate boundary conditions is close to the macroscopically expected twinned configurations with additional boundary layers localized near the twinning interfaces. In addition, we proceed to a continuum limit, show asymptotic piecewise rigidity of minimizing sequences and rigorously derive the corresponding limiting form of the surface energy.
Original languageEnglish
Title of host publicationMaterial Forming ESAFORM 2015
EditorsAldo Ofenheimer, Cecilia Poletti, Daniela Schalk-Kitting, Christof Sommitsch
PublisherWorld Scientific Publishing Co.
Pages941-943
Number of pages3
ISBN (Print)9783038354710
DOIs
Publication statusPublished - 1 Jul 2015

Publication series

NameKey Engineering Materials
PublisherWorld Scientific
Volume651-653
ISSN (Print)1013-9826

Keywords

  • Atomic Lattices
  • Geometric Rigidity
  • Martensitic Transformations
  • Twin Structures

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