Spectral database constitutive representation within a spectral micromechanical solver for computationally efficient polycrystal plasticity modelling

We present the first successful implementation of a spectral crystal plasticity (SCP) model into a spectral visco-plastic fast Fourier transform (VPFFT) full-field solver. The SCP database allows for non-iterative retrieval of constitutive solutions for a crystal of any orientation subjected to any state of deformation at every voxel representing an FFT point of the overall voxel-based polycrystalline microstructure. Details of this approach are described and validated through example case studies involving a rigid-visco-plastic response and microstructure evolution of polycrystalline copper. It is observed that the novel implementation is able to speed up the overall VPFFT calculations because the conventional Newton-Raphson iterative solution procedure for single crystals in VPFFT is replaced by the more efficient SCP constitutive representation of the solution. As a result, the implementation facilitates efficient simulations of large voxel-based microstructures. Additionally, it provides an incentive for conceiving a multi-level SCP-VPFFT computational scheme. Here, every FFT point of the model is a polycrystal whose response is calculated using a Taylor-type homogenization.