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

Georgy Kitavtsev; Stephan Luckhaus; Angkana Rüland

doi:10.4028/www.scientific.net/KEM.651-653.941

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

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 con gurations to special 1D atomic chains withposition-dependent elongation vectors for the vertical direction, we show that the structure ofground states under appropriate boundary conditions is close to the macroscopically expectedtwinned con gurations with additional boundary layers localized near the twinning interfaces.In addition, we proceed to a continuum limit, show asymptotic piecewise rigidity of minimizingsequences and rigorously derive the corresponding limiting form of the surface energy.

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Periodical:

Key Engineering Materials (Volumes 651-653)

Pages:

941-943

DOI:

https://doi.org/10.4028/www.scientific.net/KEM.651-653.941

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Online since:

July 2015

Authors:

Georgy Kitavtsev*, Stephan Luckhaus, Angkana Rüland

Keywords:

Atomic Lattices, Geometric Rigidity, Martensitic Transformations, Twin Structures

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References

[1] J. Ball and R. James. Fine phase mixtures as minimizers of energy. Arch. Rat. Mech. Anal., 100(1): 13-52, (1987).

DOI: 10.1007/bf00281246

Google Scholar

[2] K. Bhattacharya. Microstructure of martensite. Oxford Series on Materials Modelling, Oxford University Press, Oxford, (2003).

Google Scholar

[3] X. Blanc, C. Le Bris, and P. -L. Lions. From molecular models to continuum mechanics. Arch. Ration. Mech. Anal., 64: 341-381, (2002).

DOI: 10.1007/s00205-002-0218-5

Google Scholar

[4] W. E and P. B. Ming. Cauchy-Born rule and the stability of crystalline solids: static problems. Arch. Rat. Mech. Anal., 183(2): 241-297, (2007).

DOI: 10.1007/s00205-006-0031-7

Google Scholar

[5] A. Braides and M. Cicalese. Surface energies in nonconvex discrete systems. Mathematical Models and Methods in Applied Sciences, 17(07): 985 -1037, (2007).

DOI: 10.1142/s0218202507002182

Google Scholar

[6] A. Capella Kort and F. Otto. A quantitative rigidity result for the cubic to tetragonal phase transition in the geometrically linear theory with interfacial energy. In Proceedings of the Royal Edinburgh Society/A, 142(2): 273-327, (2012).

DOI: 10.1017/s0308210510000478

Google Scholar

[7] G. Friesecke, R. James, and S. Müller. A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity. Comm. Pure Appl. Math., 55(11): 1461-1506, (2002).

DOI: 10.1002/cpa.10048

Google Scholar

[8] G. Kitavtsev, S. Luckhaus, and A. Rüland. Surface energies arising in microscopic modeling of martensitic transformations. to appear in Math. Mod. Meth. Appl. Sci 2015, MPI MIS preprint 29/(2014).

DOI: 10.1142/s0218202515500153

Google Scholar