Microstructure simulation using self‐consistent clustering analysis

To capture all the individual microstructural effects of complex and heterogeneous materials in structural finite element simulations, a two‐scale simulation approach is necessary. Since the computational effort of such two‐scale simulations is extremely high, different methods exist to overcome this problem. In terms of a FFT‐based microscale simulation, one possibility is to use a reduced set of frequencies leading to a reduced numerical solution of the Lippmann‐Schwinger equation [?]. In a post‐processing step, highly resolved microstructural fields may then be reconstructed by using the compressed sensing technique [?]. Since the stress evaluation of this method is in real space and therefore not reduced, it is most beneficial in terms of linear elastic material behavior. Another very recent method to reduce the computational effort of a microscale simulation is the self‐consistent clustering analysis [?,?]. Such a self‐consistent clustering analysis is split into an offline and an online stage. Within the offline stage, the material points of the high‐fidelity representation of the unit cell are grouped into clusters with similar material behavior. Thereafter, in the online stage, a self‐consistent clustering analysis is used to solve the boundary value problem by a clustered Lippmann‐Schwinger equation. Since the generation of clusters may be based on linear elastic simulations, we propose to use a reduced set of frequencies for these simulations to improve the efficiency of the total algorithm. Elastic and elasto‐plastic composites are investigated in a small strain setting as representative simulation examples.