Crystal plasticity finite element simulations using a database of discrete Fourier transforms

In recent work, we have demonstrated the viability and computational advantages of using a compact database of discrete Fourier transforms (DFTs) for facilitating crystal plasticity solutions in cubic polycrystalline materials subjected to arbitrary deformation paths. This new DFT database approach allows for compact representation and fast retrieval of crystal plasticity solutions, which is found to be able to speed up the calculations by about two orders of magnitude. In this paper, we present the first successful implementation of this spectral database approach in a commercial finite element code to permit computationally efficient simulations of heterogeneous deformations using crystal plasticity theories. More specifically, the spectral database approach to crystal plasticity solutions was successfully integrated with the commercial finite element package ABAQUS through a user material subroutine, UMAT. Details of this new crystal plasticity spectral database-FE approach are demonstrated and validated through a few example case studies for selected deformation processes on face centered and body centered cubic metals. The evolution of the underlying crystallographic texture and its associated macroscale anisotropic properties predicted from this new approach are compared against the corresponding results from the conventional crystal plasticity finite element method. It is observed that implementing the crystal plasticity spectral database in a FE code produced excellent predictions similar to the classical crystal plasticity FE method, but at a significantly faster computational speed and much lower computational cost.