Simulation of phase combinations in shape memory alloys patches by hybrid optimization methods

Wang, L. and Melnik, R.V.N.

Applied Numerical Mathematics, 58 (4), 511--524, 2008


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.