Space-time formulation, discretization, and computational performance studies for phase-field fracture optimal control problems

Abstract

The purpose of this work are computational demonstations for a newly developed space-time phase-field fracture optimal control framework. The optimal control solution algorithm is a Newton algorithm, which is obtained with the reduced approach by eliminating the state constraint. Due to the crack irreversibility constraint, a rate-independent problem arises, which is treated by penalization and for which we utilize a space-time approach. Therein, we deal with the state, adjoint, tangent, and adjoint Hessian equations. Our fully discretized space-time optimization algorithm is presented and extensively tested with various numerical experiments.