Surface energies arising in microscopic modeling of martensitic transformations in shape-memory alloys

Kitavtsev G., Luckhaus S., Rüland A.

18th International ESAFORM Conference on Material Forming, ESAFORM 2015, Graz, Austria, 15 - 17 April 2015, vol.651-653, pp.941-943, (Full Text) identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 651-653
  • Doi Number: 10.4028/www.scientific.net/kem.651-653.941
  • City: Graz
  • Country: Austria
  • Page Numbers: pp.941-943
  • Keywords: Atomic lattices, Geometric rigidity, Martensitic transformations, Twin structures
  • Middle East Technical University Northern Cyprus Campus Affiliated: No

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.