On modeling thin inclusions in elastic bodies with a damage parameter

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3 Citations (Scopus)


In this paper, we analyze equilibrium problems for 2D elastic bodies with two thin inclusions in the presence of damage. A delamination of the inclusions from the matrix is assumed, thus forming a crack between the elastic body and the inclusions. Nonlinear boundary conditions at the crack faces are considered to prevent a mutual penetration between the faces. Weak and strong formulations of the problems are discussed. The paper provides an asymptotic analysis with respect to the damage parameter. An optimal control problem is analyzed with a cost functional to be equal to the derivative of the energy functional with respect to the crack length, and the damage parameter being a control function.

Original languageEnglish
Pages (from-to)2742-2753
Number of pages12
JournalMathematics and Mechanics of Solids
Issue number9
Publication statusPublished - 1 Sep 2019


  • crack
  • damage parameter
  • delamination
  • derivative of energy functional
  • non-penetration boundary condition
  • optimal control problem
  • Thin inclusion
  • variational inequality

State classification of scientific and technological information

  • 27.35 Mathematical models of natural Sciences and technical Sciences. Equations of mathematical physics


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