In this paper a new model of pseudo-elastic materials based on experimen tal observations of one-dimensional motions of SMA materials is introduced. The model incorporates phase fractions as an internal variable and allows for both reversible (elastic) and irreversible (plastic) modes inside the hysteresis loop. As such, the model accounts for a wider range of physical phenomena than the traditional plasticity theories. The consti tutive equations predict transitions between elastic and plastic modes through a de pendence on the time history of strain and phase fractions. These history effects are in cluded in a way that allows for easy computation.
Brokate, M. and A. Visintine.1989. "Properties of the Preisach Model for Hysteresis," J. Rein. Math., 402:1-40.
3.
Coleman, B.D. and W. Noll.1963. "The Thermodynamics of Elastic Materials with Heat Conduction and Viscosity," Arch. Rat. Mech. Anal. , 13:167-178.
4.
Hoffmann, K.H. and Z. Songmu.1988. "Uniqueness for Structural Phase Transitions in Shape Memory Alloys," Math. Meth. in the Appl. Sci., 10:145-151.
5.
Krasnosel'skii, M.A. and A.V. Pokrowskii .1989. Systems with Hysteresis (translated from the 1983 Russian edition by M. Niezgódka). Berlin : Springer-Verlag.
6.
Liang, C. and C.A. Rogers.1990. "One-Dimensional Thermomechanical Constitutive Relations for Shape Memory Materials," Jol. Intell. Mater. Syst. and Struct. , 1:207-234.
7.
Muller, I. and H. Xu.1991. "On the Pseudo-Elastic Hysteresis," Acta Metallurgica, 39:263-271.
8.
Niezgódka, M. and J. Sprekels.1988. "Global Solutions to Model of Structural Phase Transitions in Shape Memory Alloys," Math. Methods in the Appl. Sci. , 10:197-223.
9.
Plohr, B.1989. "Instabilities in Shear Flow of Viscoelastic Fluids with Fading Memory," in PDEs and Continuum Models of Phase Transitions , M. Rascle, D. Serre and M. Slemrod, eds., Springer-Verlag. Lecture Notes in Physics, 344:113-127.
10.
Renardy, M.1989. "On Rankine-Hugomot Conditions for Maxwell Liquids," J. Non-Newtonian Fluid Mechanics, 32:69-79.
11.
Tanaka, K.1986. "A Thermomechamcal Sketch of Shape Memory Effect: One-Dimensional Tensile Behavior," Res Mechanica, 18:251-263.
12.
Truesdell, C.A.1955. "Hypoelasticity," J. Rational Mech. Anal. , 4.83-133, 1019-1020
