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The exact analytical solutions have been obtained for the nonlinear problems (plane-strain and plane-stress) for the bi-material plane with an interface crack. The plane is formed by joining of two half-planes made from different materials. Mechanical properties of halfplanes are described with the model of semi-linear material. The application of this model has allowed using the methods of the complex functions in the nonlinear boundary value problems. For this particular case the problem is solved for the plane with a free interface crack at given constant nominal (Piola) stresses at infinity. The expressions for nominal stresses, Cauchy stresses and displacements are obtained. From the general solutions the asymptotic expansions of these functions have been constructed in vicinities of crack tips. It is established that in the nonlinear problem of uniaxial extension of a plane with a free crack the formulas which give the crack disclosing differ by a constant factor from the formulas of linear elasticity. The stress intensity factors (SIF) of nonlinear and linear problems coincide. The nominal stresses have the root singularity at the tips of a crack; the Cauchy stresses have no singularity.
Translated title of the contributionMathematical modeling of the deformation of composite plane with interface crack for semi-linear materia
Original languageRussian
Pages (from-to)89-102
Number of pages14
Journal ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ
Volume14
Issue number2
DOIs
StatePublished - 2018

    Scopus subject areas

  • Control and Optimization
  • Applied Mathematics
  • Computer Science(all)

    Research areas

  • bi-material plane, plane-strain problem, plane-stress problem, method of complex functions, interface crack, semi-linear material., Semi-linear material, Bi-material plane, Plane-strain problem, Interface crack, Method of complex functions, Plane-stress problem

ID: 35361146