SMA Modeling

SMA Modeling: Multivariant Model

To describe SMA thermomechanical behavior based fundamentally upon the underlying crystallographic phase transformation, our group has developed the Multivariant Model. This approach uses thermodynamics to describe the transformation and micromechanics to estimate the interaction energy due to phase transformation. The model starts with the crystal lattice parameters of the material and knowledge of the martensitic variants and their self-accommodated structure. The essential set of equations which are solved in the Multivariant model are the n simultaneous differential equations (one for each variant)


The transformation strain of each variant, (n=1,2, ..., 24), is calculated from the basic crystallographic information on the habit plane normals, n, and transformation directions, m, for a given material using the phenomenological theory of martensite crystallography. Stress and temperature are external driving forces, Fext, on the system; Fwall (l terms) simply represents constraints to keep martensite fractions non-negative and the total less than 100%, and FC is the frictional resistance force. The system of differential equations is solved numerically for each grain in a polycrystal. The multivariant model has been used recently to simulate the texture evolution of NiTi samples and shows excellent agreement with experiments (Fig. 1).

two poles of NiTi

Researcher on this project:

Aaron Stebner

Relevant Publications:

Gao, X. J., D. S. Burton, D. Brown, and L. C. Brinson, Reorientation in Shape Memory Alloys: Multivariant Model Simulations and Neutron Diffraction Studies, to be submitted to Acta Materialia, (2007).

X. Gao and L. C. Brinson, A Simplified Multivariant SMA Model Based on the Invariant Plane Nature of Martensitic transformation, J. Intell. Matl Syst. Struct, 13 (12): pp. 795-810 (2002).

Gao, X., M. Huang, and L.C. Brinson, A Multivariant Micromechanical Model for SMAs: Part 1: Crystallographic issues for single crystal model. Int. Journal of Plasticity, vol. 16, pp. 1345-1369 (2000).

Huang, M.S., X. Gao, and L.C. Brinson, A Multivariant Micromechanical Model for SMAs: Part 2: Polycrystal Model. Int. J. Plasticity, vol. 16, pp. 1371-1399 (2000).

Huang, M. and L. C. Brinson, A Multivariant Model for Shape Memory Alloys, Journal of the Mechanics & Physics of Solids, vol. 46:8, pp. 1379-1409, (1998).

Advanced Materials Laboratory, Department of Mechanical Engineering
Robert R. McCormick School of Engineering and Applied Science, Northwestern University
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