Numerical model reduction for computational homogenization of polycrystals

Research Project, 2020 – 2023

This project targets efficient modeling of polycrystalline (metallic) materials, with applications in engineering and materials science. At the microscale, we consider crystal-(visco)plasticity for modeling inelastic deformations while accounting for lattice orientations and grain-boundary interaction. A gradient-enhanced formulation is adopted to properly capture grain-size effects. Using computational homogenization, the effective stress-strain response is obtained from finite element analysis on Representative Volume Elements (RVEs). The latter can be used either in a so-called “finite element squared” (FE2) framework to concurrently solve a macroscopic problem, or in order to conduct “Virtual Testing”, e.g. to predict the effective yield surface. These procedures are vastly computationally demanding due to the complexity and size of the RVE-problems.We propose to develop Numerical Model Reduction (NMR) for the discrete RVE-problems. By constructing a suitable (reduced) approximation basis, the computational cost is significantly reduced. Key ingredients are the development of error estimates and the pertinent adaptation of the reduced basis. The NMR procedures will be applied and implemented in "Virtual Testing" as well as for full-fledged FE2 analysis. As a special case, a Discrete Grain model will be developed, where the reduced basis pertains to the deformation of each grain, allowing for efficient interpretation of in-site neutron diffraction experiments.