Addressing biases in spectral databases for increasing accuracy and computational efficiency of crystal plasticity computations

Abstract

Spectral databases of crystal plasticity solutions stored as discrete Fourier transforms (DFTs) have now been used for over a decade to speed-up the crystal plasticity simulations. These approaches have demonstrated impressive computational advantages over the conventional numerical approaches that explicitly solve the governing constitutive equations. However, their implementation in finite element models (FEM) referred to as spectral crystal plasticity finite element method (SCPFEM) framework has encountered significant hurdles mainly related to instabilities in jacobian calculations leading to convergence issues in solving the governing equilibrium equations. In this work, these main hurdles encountered are tracked to certain biases introduced in the formulation of the spectral databases. These biases are related to the choices made in the selection of the independent diagonal components of the deviatoric stress tensor and the ordering of the eigenvalues of the plastic stretching tensor. Specific strategies have been designed and implemented to address these biases such as, generating separate DFT database for all three diagonal components of deviatoric stress tensor, and standardizing the assignment of eigenvalues of the plastic stretching tensor among the other improvements. These improvements to the spectral databases have been shown to improve markedly the accuracy of the database solutions for both the stress-strain responses as well as the jacobians needed in finite element computations. The benefits of the improved databases are demonstrated with selected case studies.