This paper describes a new approach for the extraction of the single crystal elastic stiffness parameters from polycrystalline samples using spherical nanoindentation and orientation measurements combined with finite element simulations. The first task of this new approach involves capturing efficiently the functional dependence of the indentation modulus on the lattice orientation at the indentation site and the unknown single crystal elastic constants.

          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.

          In recent work, we have demonstrated the viability and computational advantages of DFT-based spectral databases for facilitating crystal plasticity solutions in face-centered cubic (fcc) metals subjected to arbitrary deformation paths. In this paper, we extend and validate the application of these novel ideas to body-centered cubic (bcc) metals that exhibit a much larger number of potential slip systems.

          In this paper, we present the first implementation of the novel localization relationships, formulated in the recently developed mathematical framework called materials knowledge systems (MKS), into a finite element tool to enable hierarchical multiscale materials modeling. More specifically, the MKS framework was successfully integrated with the commercial finite element package ABAQUS through a user materials subroutine. In this new MKS-FE approach, information is consistently exchanged between the microscale and macroscale levels in a fully coupled manner.

          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.