Crystal plasticity simulations using discrete Fourier transforms

In this paper, we explore efficient representation of all of the functions central to crystal plasticity simulations in their complete respective domains using discrete Fourier transforms (DFTs). This new DFT approach allows for compact representation and fast retrieval of crystal plasticity solutions for a crystal of any orientation subjected to any deformation mode. The approach has been successfully applied to a rigid-viscoplastic Taylor-type model for face-centered cubic polycrystals. It is observed that the novel approach described herein is able to speed up the conventional crystal plasticity computations by two orders of magnitude. Details of this approach are described and validated in this paper through a few example case studies.