MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Surface Energies Arising in Microscopic Modeling of Martensitic Transformations

Georgy Kitavtsev, Stephan Luckhaus and Angkana Rüland


In this paper 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.

MSC Codes:
74N05, 74N15, 74N20
martensitic transformations, atomic lattices, twin structures, geometric rigidity

Related publications

2015 Repository Open Access
Georgy Kitavtsev, Stephan Luckhaus and Angkana Rüland

Surface energies arising in microscopic modeling of martensitic transformations

In: Mathematical models and methods in applied sciences, 25 (2015) 4, pp. 647-683