Spectral methods for full-field micromechanical modelling of polycrystalline materials

Modelling the mechanical behavior of polycrystalline materials based on their evolving microstructure and the anisotropic properties of their constituent single crystal grains is nowadays an indispensable tool to establish physically-based relationships between processing, structure and properties of this ubiquitous type of materials. These models have found multiple applications in Material Science, Mechanics of Materials, and Earth Sciences. This article reviews the specialization to polycrystalline materials of a spectral formulation developed in the last two decades to efficiently solve the micromechanical behavior of heterogeneous materials. This review provides a consolidated account, using a unified notation, of the various numerical implementations of the spectral formulation for polycrystalline materials deforming in different constitutive regimes, each of which requires specific numerical strategies. Examples are given that illustrate these implementations for each constitutive behavior, as well as comparisons with other models, and applications to different materials, including the use of experimental data for input of the calculations and validation of the model predictions.