Numerically robust spectral methods for crystal plasticity simulations of heterogeneous materials

•Efficient spectral methods are developed based on direct and mixed variational approaches.•Equivalence of the proposed formulations with the original formulation is demonstrated.•Examples show improved performance for highly heterogeneous and non-linear materials.•Guidelines for composing favourable solution strategies are provided.

Efficient spectral methods are developed to predict the micromechanical behaviour of plastically deforming heterogeneous materials. The direct and mixed variational conditions for mechanical equilibrium and strain compatibility are formulated in a framework that couples them to a general class of non-linear solution methods. Locally evolving micromechanical fields in a sheared polycrystalline material governed by a phenomenological crystal plasticity constitutive law are used to validate the methods, and their performance at varying material heterogeneities is benchmarked. The results indicate that the solution method has a dominant influence on performance and stability at large material heterogeneities, and significant improvements over the conventional fixed-point approach are obtained when higher-order solution methods are employed. Optimal solution strategies are devised based on this and applied to an idealised dual-phase polycrystalline aggregate.