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.

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