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Differential, Energetic, and Metric Formulations for Rate-Independent Processes

Part of the Lecture Notes in Mathematics book series (LNMCIME,volume 2028)

Abstract

In these notes we want to give an overview of the recently developed theory for rate-independent systems. Such systems are used to model hysteresis, dry friction, elastoplasticity, magnetism, and phase transformation, and they are characterized by the fact that the changes of the state are driven solely by changes of the loading. More specifically, if the loading profile is applied with a factora faster to the system, then rescaling the solution with the same factora gives again a solution.

Keywords

  • Parametrized Solution
  • Arclength Parametrization
  • Dissipation Potential
  • Quasistatic Evolution
  • Energetic Formulation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Acknowledgements

The research was partially supported by DFG via Research Unit FOR 787 MicroPlast (Project Mie 459/5, Regularizations and relaxations of time continuous problems in plasticity). The author is indebted to Tomaáš Roubíček, Riccarda Rossi, Giuseppe Savaré, Marita Thomas, and Sergey Zelik for helpful and stimulating discussions. He thanks Olga Kuphal and Riccarda Rossi for their careful proofreading and for improving the English. Finally, he thanks Luigi Ambrosio, Giuseppe Savaré, and CIME for organizing the wonderful Summer School on Nonlinear Partial Differential Equations and Applications in Cetraro.

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Mielke, A. (2011). Differential, Energetic, and Metric Formulations for Rate-Independent Processes. In: Nonlinear PDE’s and Applications. Lecture Notes in Mathematics(), vol 2028. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21861-3_3

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