Optimal Control of Dissipative Solids: Viscosity Limits and Non-Smooth Algorithms
The proposed project concerns the optimal control of dissipative solids. Point of departure is a thermodynamically consistent material model which takes into account damage effects as well as thermo-elastoplasticity. A modern solution theory for such systems with rate-independent components is based on so-called balanced viscosity solutions whose existence is proved by means of viscous regularization and a subsequent passage to the limit in the viscosity parameters.
Within the proposed project, we intend to analyze the optimization of damage and thermo-plastic deformation processes under this solution concept. Besides the existence of optimal controls, we are mainly interested in the approximability of locally optimal controls by viscous regularization.The rate-dependent, viscous problems have a physical meaning in their own right, and they are still non-smooth in the sense that the associated control-to-state operator is, in general, not Gateaux differentiable. Moreover, the viscous problems serve as a basis for the development of an efficient optimization algorithm, a bundle method in function space. To apply it, elements of the subdifferential in the sense of Clarke are to be determined on the basis of directional derivatives for the viscous model problems.
By using a path-following approach for vanishing viscosity, we expect to be able to compute optimal solutions even of the associated rate-independent problems.
No publications from this project yet.
Christian Meyer, Michael Sievers: A-Priori Error Analysis of Local Incremental Minimization Schemes for Rate-independent Evolutions (SPP1962-115, 07/2019, [bib])
Dorothee Knees: Convergence Analysis of Time-Discretisation Schemes for Rate-Independent Systems (SPP1962-063, 07/2018, [bib])
Christian Meyer, Michael Sievers: Finite Element Discretization of Local Minimization Schemes for Rate-Independent Evolutions (SPP1962-046, 12/2017, [bib])
Roland Herzog, Ailyn Stötzner: Hadamard Differentiability of the Solution Map in Thermoviscoplasticity (SPP1962-044, 11/2017, [bib])
Dorothee Knees, Riccarda Rossi, Chiara Zanini: Balanced Viscosity Solutions to a Rate-Independent System for Damage (SPP1962-018, 04/2017, [bib])
Project Related News
Jul 04, 2019 : New preprint submitted
Christian Meyer submitted the preprint SPP1962-115, A-Priori Error Analysis of Local Incremental Minimization Schemes for Rate-independent Evolutions
Sep 21, 2018 : PhD thesis defended
Ailyn Stötzner defended her doctoral dissertation on "Optimal Control of Thermoviscoplasticity" at Technische Universität Chemnitz.
Nov 01, 2016 : Welcome to our new project member
Stefanie Thomas joins project 9.
Oct 10, 2016 : Welcome to our new project member
Ailyn Stötzer joins project 9.