We develop a continuum theory for martensitic phase transformations in which explicit use is made of atomistic calculations based on density functional theory. Following the work of Rabe and coworkers, branches of the phonon-dispersion relation with imaginary frequencies are selected to construct a localized basis tailored to the symmetry of the crystal lattice. This so-called Wannier basis helps to construct an effective Hamiltonian of a particularly simple form. We extend the methodology by incorporating finite deformations and passing the effective Hamiltonian fully to continuum level. The developments so far are implemented on the shape memory material NiTi.
Bibliographical noteFunding Information:
The work of MT was supported by The Netherlands Organization for Scientific Research (NWO) through Stipent S69-100 and by the Dutch Technology Foundation STW through VENI-grant DLR.5813. RDJ thanks AFOSR/MURI (F49620-98-1-0433) for support. The work also benefited from the support of NSF (DMS-0074043) and ONR (MURI N000140110761). Courtesy of the Army Center: This work was supported in part by the AHPCRC under the auspices of the Department of the Army, ARL, under the cooperative agreement number DAAD19-01-2-0014. The content does not necessarily reflect the position or the policy of the US government, and no official endorsement should be inferred.
Copyright 2008 Elsevier B.V., All rights reserved.
- Continuum free energy
- Effective Hamiltonian
- Martensitic phase transformation
- Phonon-dispersion relation
- Wannier basis