Spektralmethoden für kugelförmige repräsentative Volumenelemente
Mechanische Eigenschaften von metallischen Werkstoffen und ihre mikrostrukturellen Ursachen
Zusammenfassung der Projektergebnisse
For many engineering applications, the homogenized material behavior needs to be known. The high computational efforts needed to obtain the homogenized response for materials with complex internal microstructure via computational homogenization require often to compromise on the size of the RVE. In this project, the combination of two approaches to speed up the calculations, namely 1) using fast spectral methods for the solution of mechanical equilibrium and 2) using optimized spherical volume elements, is investigated. Spectral methods gained popularity in computational micromechanics due to their beneficial convergence behavior. Spherical volume elements are also numerically beneficial for non-periodic microstructures as they reduce the surface-area-to-volume ratio. To this end, several solution approaches for quasistatic solid mechanics in polar and spherical coordinates have been investigated. During the project, it was found that the amount of spectral solution schemes on spherical domains is large and only a few of them have been implemented and tested. It was also found that the transfer of approaches that are successful in neighboring domains to the field of solid mechanics is usually difficult. One solution approach, single-domain spectral solver for spatially nonsmooth differential equations has been pursued in detail. This solver is currently limited to two-dimensional situations and isotropic and elastic materials. Hence, for use in realistic situations an extension to three dimensions and the ability to handle more complex material laws is required. In addition to the work on the solver, which is implemented in MATLAB, finite element modeling has been used to provide a set of benchmark models for three-dimensional simulations.
