Wavelet-FFT-based multiscale mechanics

• Applicant: Privatdozent Dr.-Ing. Tobias Kaiser
• Subject Area: Mechanics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 548608747

The effective mechanical material response at an engineering length scale is a manifestation of the underlying microstructure and of lower-scale processes. This lower-scale information is accounted for in computational multiscale approaches by exploiting detailed representations of the underlying material microstructure and material models that have been developed at the level of individual phases. To this end, classic macroscale material models are substituted by microscale boundary value problems. Evidently, the repetitive solution of these unit cell problems in each macroscale integration point is associated with a significant computational effort in terms of CPU-time and memory requirements. This particularly holds true when a nonlinear history-dependent material behaviour applies. To address these challenges, tailored solution approaches that make use of the specific structure of the unit cell problem are proposed with FFT-based spectral approaches being amongst the most promising ones. In the present work, state-of-the-art spectral solvers are revisited and enhanced by making use of the multiresolution nature and the inbuilt adaptivity of wavelets. In particular: • Hybrid wavelet-FFT- and wavelet-nuFFT approaches for the efficient solution of microscale boundary value problems in a general three-dimensional setting that account for inelastic history-dependent material behaviour of the microscale constituents are developed. The approaches operate on irregular, adaptively refined grids and a substantial reduction in computational costs compared to state-of-the-art spectral approaches is expected by significantly reducing the number of material model evaluations. • The severe memory requirements associated with the storage of microscale history variable fields are strongly alleviated by establishing adaptive wavelet-based compression algorithms.

• DFG Programme: Research Grants
• International Connection: Netherlands
• Cooperation Partners: Professor Dr. Marc G. D. Geers; Professor Dr. Joris J. C. Remmers