An image analysis technique was employed to document the layered parallel microstructures observed during tensile tests of CuAlNi single crystal shape memory alloys. The evolution of the microstructures during the stress induced martensitic transformation can be then well studied quantitatively by the evolution of the phase character function and its suitable averages. The results indicated clearly that the stress induced martensite transformation should consist three periods, initial formation, mixed formation and growth, merging due to growth. Euler-Lagrange equations for the minimizers of some one-dimensional energy functional were also studied for two types of two-well strain energy functions, the piecewise quadratic energy function and a smooth polynomial. The cell exclusive genetic algorithm was adapted to solve the nonlinear algebraic equations in the first case. The homotopy analysis method was used in the second case to find accurate series solutions. Multi-interface microstructures were obtained in both cases. The methods, especially the homotopy analysis seemed to be quite powerful to solve the nonlinear equations even with large number of interfaces.

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