Asymptotics of anisotropic weakly curved inclusions in an elastic body

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Abstract

Under study are the boundary value problems describing the equilibrium of twodimensional elastic bodies with thin anisotropic weakly curved inclusions in presence of separations. The latter implies the existence of a crack between the inclusion and the matrix. Nonlinear boundary conditions in the form of inequalities are imposed on the crack faces that exclude mutual penetration of the crack faces. This leads to the formulation of the problems with unknown contact area. The passage to limits with respect to the rigidity parameters of the thin inclusions is inspected. In particular, we construct the models as the rigidity parameters go to infinity and analyze their properties.

Original languageEnglish
Pages (from-to)88-98
Number of pages11
JournalJournal of Applied and Industrial Mathematics
Volume11
Issue number1
DOIs
Publication statusPublished - 1 Jan 2017

Keywords

  • crack
  • elastic body
  • limit model
  • nonlinear boundary condition
  • thin inclusion

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