Adaptive Model Order Reduction in Solid Mechanics for Elasto-Plastic Boundary Value Problems

Model Order Reduction (MOR) techniques serve as powerful tools to reduce the computational costs of numerical simulations with a large number of degrees of freedom. Especially for problems incorporating non-linear material behavior, such as plasticity, or materials which exhibit heterogeneous structures on the microscale, MOR techniques offer the potential to significantly speedup the solution process. Yet, for projection-based MOR techniques, a challenge remains in the choice of basis in the context of non-linear problems. The present thesis introduces a projection-based MOR scheme for small strain elasto-plasticity in the framework of the Finite Element Method (FEM). The consideration of material non-linearities in the reduced order model is realized by an adaptive scheme for updating the basis in different stages of the simulation. Extensions of the update procedure in comparison to existing works in this field are presented. In respective numerical studies, the performance of the reduced order model with respect to reference simulations are demonstrated based on academical and microstructural examples.