Modeling Introduction of Rigid Sphere into Layered Elastic Body

  • P. OgarEmail author
  • A. Kozhevnikov
  • V. Kushnarev
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


On the basis of a simplified rigid model of a layered elastic body, an engineering technique for determining the parameters of a contact is proposed for the indentation of a spherical indenter into it. The model is based on the dependence of the displacement of the points of the half-space along the axis of symmetry on the magnitude of the applied distributed load. The reduced elasticity modulus and the Poisson’s ratio are determined depending on the elastic properties of the base and coating materials, the thickness of the coating, and the radius of the contact area. Equations are given for determining the parameters of a contact when a spherical indenter is indented into a layered body. The obtained results are compared with the exact solution of the spatial axisymmetric problem for describing the stress-strain state in an elastic layer when a spherical indenter is indented into it, obtained by A. P. Makushkin using the Fourier–Bessel integral transformation method.


Layered elastic body Layered half-space Reduced elastic modulus Indentation of a sphere 


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Bratsk State UniversityBratskRussia

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