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On Existence of Optimal Solutions to Boundary Control Problem for an Elastic Body with Quasistatic Evolution of Damage

  • Peter I. KogutEmail author
  • Günter Leugering
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 211)

Abstract

We study an optimal control problem for the mixed boundary value problem for an elastic body with quasistatic evolution of an internal damage variable. We use the damage field \(\zeta =\zeta (t,x)\) as an internal variable which measures the fractional decrease in the stress-strain response. When \(\zeta =1\) the material is damage-free, when \(\zeta =0\) the material is completely damaged, and for \(0<\zeta <1\) it is partially damaged. We suppose that the evolution of microscopic cracks and cavities responsible for the damage is described by a nonlinear parabolic equation, whereas the model for the stress in elastic body is given as \(\varvec{\sigma }=\zeta (t,x) A\mathbf {e}({\mathbf {u}})\). The optimal control problem we consider in this paper is to minimize the appearance of micro-cracks and micro-cavities as a result of the tensile or compressive stresses in the elastic body.

Keywords

Weak Solution Optimal Control Problem Displacement Field Elastic Body Radon Measure 
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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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Differential EquationsDnipropetrovsk National UniversityDnipropetrovskUkraine
  2. 2.Institüt für Angewandte Mathematik Lehrstuhl II UniversitätErlangenGermany

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