Space-time modeling, analysis, and finite element simulations of phase-field fracture optimal control problems
In this presentation, we will introduce novel space-time formulations for phase-field fracture optimal control problems.
The main goal is to control the propagation of fractures, modeled by phase-field, towards desired paths using a tracking-type cost functional.
We establish a theoretical framework that includes the selection of appropriate function spaces, the derivation of auxiliary equations, discretization using Galerkin methods, and computational experiments.
We explore two different formulations, each handling constraints and crack irreversibility in unique ways.
The first formulation uses a penalty approach to address crack irreversibility, leading to an equality-constrained NLP, solved using the reduced approach. The second formulation treats both, the phase-field and optimal control problems, as abstract NLPs,
allowing us to rigorously prove regularity under certain conditions and derive the corresponding KKT systems.
