  In this paper, phase combinations among martensitic variants in shape memory
alloys patches and bars are simulated by a hybrid optimization methodology. The
mathematical model is based on the Landau theory of phase transformations. Each
stable phase is associated with a local minimum of the free energy function,
and the phase combinations are simulated by minimizing the bulk energy. At low
temperature, the free energy function has double potential wells leading to
non-convexity of the optimization problem. The methodology proposed in the
present paper is based on an initial estimate of the global solution by a
genetic algorithm, followed by a refined quasi-Newton procedure to locally
refine the optimum. By combining the local and global search algorithms, the
phase combinations are successfully simulated. Numerical experiments are
presented for the phase combinations in a SMA patch under several typical
mechanical loadings.
