Space-time adaptivity and model order reduction with digital image/volume correlation with application to parameter identification in phase-field fracture

This project explores advanced computational techniques to enhance the simulation of fracture propagation in brittle materials, focusing on space-time adaptivity and model order reduction within the framework of phase-field fracture simulations. The project encompasses two core objectives: firstly, the development of a robust and efficient solver using the Finite Element Method (FEM) and the deal.II library, incorporating matrix-free geometric multigrid methods and space-time adaptivity to effectively address challenges in solving nonlinear partial differential equations (PDEs); secondly, the application of this solver to advanced tests to enable parameter identification based on experimental data. The project is structured around these primary goals, involving mathematical analysis of matrix-free multigrid methods applied to the Oseen and Navier-Stokes equations, parameter identification in complex fracture simulations such as the Carpiuc and wedge-splitting tests, the integration of space-time adaptivity for improved simulation accuracy and efficiency, and the exploration of model order reduction (MOR) strategies for nonlinear phase-field fracture problems. Spanning three years, the project includes collaborative international research stays and aims to significantly advance computational mechanics, particularly in fracture mechanics, thereby providing a foundation for more efficient simulations and improved material design.

Doctoral Researcher: Leon Kolditz

Scientific Advisor: Thomas Wick