Surface Energies Arising in Microscopic Modeling of Martensitic Transformations
Georgy Kitavtsev, Stephan Luckhaus, and Angkana Rüland
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Submission date: 21. Feb. 2014
published in: Mathematical models and methods in applied sciences, 25 (2015) 4, p. 647-683
DOI number (of the published article): 10.1142/S0218202515500153
MSC-Numbers: 74N05, 74N15, 74N20
Keywords and phrases: martensitic transformations, atomic lattices, twin structures, geometric rigidity
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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.