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Simulation of phase transformations in polycrystalline shape memory alloys using fast Fourier transforms

. The properties of shape memory alloys (SMA) are mainly inﬂuenced by phase transformations between austenite and martensite. The complex material behavior is described by a variational method which describes the evolution of the phase fractions. We combined the method with a microstructural analysis based on fast Fourier transformations. Such a highly resolved microstructural analysis comes along with a high computational eﬀort. To reduce the later one, we propose a model order reduction technique that uses just a reduced set of Fourier modes, which is adapted to the underlying microstructure. The presentation of the theoretical background as well as of the implemented algorithm is followed by numerical results that underline the performance of our method.