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Rate-Independent Systems and Their Viscous Regularizations: Analysis, Simulation, and Optimal Control

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Non-Smooth and Complementarity-Based Distributed Parameter Systems

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 172))

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Abstract

This chapter provides a survey on the analysis, simulation, and optimal control of a class of non-smooth evolution systems that appears in the modeling of dissipative solids. Our focus is on models that include internal constraints, such as a flow rule in plasticity, and that account for the temperature dependence of the respective materials. We discuss here two cases, namely purely rate-independent models and viscously regularized models coupled to the temperature equation.

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Acknowledgements

The research of this work was carried out in Project P09 (Optimal Control of Dissipative Solids: Viscosity Limits and Non-Smooth Algorithms) within the DFG Priority Program SPP 1962 (Non-Smooth and Complementarity-Based Distributed Parameter Systems: Simulation and Hierarchical Optimization). The support by the DFG is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Institute for Applied Mathematics, University of Heidelberg, Heidelberg, Germany

    Roland Herzog

  2. Institute for Mathematics, University of Kassel, Kassel, Germany

    Dorothee Knees & Stephanie Thomas

  3. TU Dortmund, Faculty for Mathematics, Dortmund, Germany

    Christian Meyer & Michael Sievers

  4. TU Chemnitz, Faculty of Mathematics, Chemnitz, Germany

    Ailyn Stötzner

Authors
  1. Roland Herzog
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  6. Stephanie Thomas
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Corresponding author

Correspondence to Dorothee Knees .

Editor information

Editors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    Michael Hintermüller

  2. Institute for Applied Mathematics, University of Heidelberg, Heidelberg, Germany

    Roland Herzog

  3. Lehrstuhl für Mathematik VII, Julius-Maximilians-Universität Würzburg, Würzburg, Germany

    Christian Kanzow

  4. Department of Mathematics, Technical University of Munich, Garching b. München, Germany

    Michael Ulbrich

  5. Fachbereich Mathematik, Technische Universitaet Darmstadt, Darmstadt, Germany

    Stefan Ulbrich

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Herzog, R., Knees, D., Meyer, C., Sievers, M., Stötzner, A., Thomas, S. (2022). Rate-Independent Systems and Their Viscous Regularizations: Analysis, Simulation, and Optimal Control. In: Hintermüller, M., Herzog, R., Kanzow, C., Ulbrich, M., Ulbrich, S. (eds) Non-Smooth and Complementarity-Based Distributed Parameter Systems. International Series of Numerical Mathematics, vol 172. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-79393-7_6

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