N-site Modelling of a 3D Viscoplastic Polycrystal Using Fast Fourier Transform

Abstract

We present a formulation to compute the local response of elastic and viscoplastic anisotropic 3D polycrystals based on the Fast Fourier Transform (FFT) method. This FFT method can be applied to a heterogeneous periodic medium but also to structures in which the size of the heterogeneities is small compared with the size of the specimen. It provides an exact solution of the Lippmann-Schwinger equations and has better numerical performance than small-scale FEM. The results of this n-site FFT formulation are here compared with the predictions obtained for the same microstructure with the I-site self consistent model.