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Mathematics and Mechanics of Solids
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On the Correspondence between Micromechanical Models for Isothermal Pseudoelastic Response of Shape Memory Alloys and the Preisach Model for Hysteresis

D. C. Lagoudas

A. Bhattacharyya

Center for Mechanics of Composites, Aerospace Engineering Department, Texas A & M University, College Station, 7X 77843-3141

In this work, the authors derive the weighting functions of the Preisach model of hysteresis (used for real-time control applications) corresponding to the uniaxial isothermal psuedoelastic response of an SMA polycrystal. A uniform distribution of single crystals is taken to constitute the polycrystal. The assumed phase transformation criterion is based on the shear component of the traction vector on a habit plane reaching a threshold value. The derived weighting functions are correlated analytically to the isothermal transformation properties of the single crystals and through the orientation distribution function to the polycrystalline SMA. The purpose of the present work is to provide a point of departure from the traditional practice by which the weighting functions are being determined from experimental data on polycrystalline SMA actuators.

Mathematics and Mechanics of Solids, Vol. 2, No. 4, 405-440 (1997)
DOI: 10.1177/108128659700200403
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[Abstract] [PDF]