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Phys. Rev. Lett. 74, 746–749 (1995)

Free Boundary Conditions at Austenite-Martensite Interfaces

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O. P. Bruno
School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160

P. H. Leo
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, Minnesota 55455

F. Reitich
Center for Research in Scientific Computation and Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205

Received 25 August 1994; published in the issue dated 30 January 1995

A mathematical model is presented for the dynamical strain-stress response of shape memory wires. This model is based on a free boundary problem for the heat equation which incorporates bistable potentials together with a physical constant, independent of stress or temperature, which accounts for mechanically dissipative processes. An expression in closed form is derived for one of the most important observables, namely the width of the hysteresis loops as a function of the elongation rates. Excellent agreement with experimental results is observed.

© 1995 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.74.746
DOI:
10.1103/PhysRevLett.74.746
PACS:
64.70.Kb, 65.50.+m, 82.65.Dp