Spectral Solvers for Crystal Plasticity and Multi-physics Simulations

The local and global behavior of materials with internal microstructure is often investigated on a (representative) volume element. Typically, periodic boundary conditions are applied on such “virtual specimens” to reflect the situation in the bulk of the material. Spectral methods based on Fast Fourier Transforms (FFT) have been established as a powerful numerical tool especially suited for this task. Starting from the pioneering work of Moulinec and Suquet, FFT-based solvers have been significantly improved with respect to performance and stability. Recent advancements of using the spectral approach to solve coupled field equations enable also the modeling of multiphysical phenomena such as fracture propagation, temperature evolution, chemical diffusion, and phase transformation in conjunction with the mechanical boundary value problem. The fundamentals of such a multi-physics framework, which is implemented in the Düsseldorf Advanced Materials Simulation Kit (DAMASK), are presented here together with implementation aspects. The capabilities of this approach are demonstrated on illustrative examples.