Optimal Control for Phase-Field Fracture: Algorithmic Concepts and Computations

Abstract

In this work, we present an algorithmic realization for computing optimal control problems with quasi-static phase-field fracture as a PDE constraint. The phase-field fracture problem is formulated in a quasi-monolithic approach resulting in a nonlinear forward problem. The optimization problem is formulated within a reduced approach, where the state variable is eliminated. To this end, a globalized reduced Newton algorithm is employed. Our algorithmic developments are substantiated with a numerical example.