Optimal Control of Phase-Field Fracture Evolution

Optimal Control of Phase-Field Fracture Evolution

September 28th, 2018 12:00 – 14:00
Waste4Think Room at DeustoTech

Prof. Dr. Winnifried Wollner

Technische Universität Darmstadt, Germany

Within this talk, we will address optimization problems governed by phase-field fracture/damage processes. The presence of an irreversibility of the fracture growth gives rise to a nonsmooth system of equations. To derive optimality conditions we introduce an additional regularization and show that the resulting optimization problem is well-posed. We will discuss first order necessary optimality conditions and the corresponding constraint qualifications needed. Finally, we will see, that a quadratic approximation to the optimization problem is always solvable.

Further, to allow for the analysis of finite dimensional approximations to this problem, we provide a new regularity resulting providing improved differentiability of elliptic systems with non-smooth coefficients. We will finally give an outlook on the resulting discretization error estimates.

This is joint work with:
Robert Haller-Dintelmann, Hannes Meinlschmidt, Masoumeh Mohammadi, Ira Neitzel, Thomas Wick.