Statistically Compatible Hyper-Reduction for Multiphysics Homogenization

• Applicant: Professor Dr.-Ing. Stephan Wulfinghoff
• Subject Area: Mechanics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 550055706

Computational homogenization via the FE2-method (FE: Finite Element) has experienced a tremendous development during the past two decades. Nevertheless, much effort continues to be devoted to using model order reduction techniques to reduce the enormous computational costs. A related new hyper-reduction method for computational homogenization, which has been recently published by the applicant, shows excellent performance. The method is fundamentally different from other hyper-reduction methods, as the integration points are defined in strain space based on the statistics of the strain fluctuations rather than in real space. This provides greater flexibility in the choice of integration points and unlocks additional potential to further improve the performance of reduced order models. So far, the new method is largely unexplored and has been applied only to mechanics. The aim of this proposal is to investigate the method’s performance for the multi-physics computational homogenization of functional materials. One example of interest is given by multiferroic composites, which enable to tailor a superior macroscopic magnetoelectric coupling behavior through a beneficial design of the microstructure. Another example is given by materials with non-standard rate effects arising from non-negligible transient effects on the microscale. The homogenization of such materials requires extended scale-transition techniques and is currently a very active field of research. The aim of this proposal is the development of conceptually new statistically based hyper-reduction methods for multi-physics computational homogenization with special focus on multiferroic materials and materials with non-negligible micro-transient effects.

• DFG Programme: Research Grants