On crack propagations in elastic bodies with thin inclusions

A. M. Khludnev, T. S. Popova

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

The paper concerns an analysis of a crack propagation phenomena for an elastic body with thin inclusions and cracks. In the frame of free boundary approach, we investigate a dependence of the solutions on a rigidity parameter of the inclusion. A passage to the limit is justified as the parameter goes to infinity. Derivatives of the energy functionals are found with respect to the crack length for the models considered with different rigidity parameters. The Griffith criterion is used to describe a crack propagation. In so doing, an optimal control problem is investigated with a rigidity parameter being a control function. A cost functional coincides with a derivative of the energy functional with respect to the crack length. A solution existence is proved.

Original languageEnglish
Pages (from-to)586-599
Number of pages14
JournalSiberian Electronic Mathematical Reports
Volume14
DOIs
Publication statusPublished - 1 Jan 2017

Keywords

  • Crack
  • Delamination
  • Nonpenetration boundary condition
  • Optimal control
  • Semirigid inclusion
  • Thin elastic inclusion
  • Timoshenko beam

Fingerprint Dive into the research topics of 'On crack propagations in elastic bodies with thin inclusions'. Together they form a unique fingerprint.

Cite this