Acta Mechanica Sinica

, Volume 29, Issue 2, pp 196–201 | Cite as

Analytical solution of axisymmetric contact problem about indentation of a circular indenter into a soft functionally graded elastic layer

  • Sergey Volkov
  • Sergey AizikovichEmail author
  • Yue-Sheng Wang
  • Igor Fedotov
Research Paper


The paper addresses a contact problem of the theory of elasticity, i.e., the penetration of a circular indenter with a flat base into a soft functionally graded elastic layer. The elastic properties of a functionally graded layer arbitrarily vary with depth, and the foundation is assumed to be elastic, yet much harder than a layer. Approximated analytical solution is constructed, and it is shown that the solutions are asymptotically exact both for large and small values of characteristic dimensionless geometrical parameter of the problem. Numerical examples are analyzed for the cases of monotonic and nonmonotonic variations of elastic properties. Numerical results for the case of homogeneous layer are compared with the results for nondeformable foundation.


Contact problems Indentation Functionally graded layer 


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Sergey Volkov
    • 1
  • Sergey Aizikovich
    • 1
    • 2
    Email author
  • Yue-Sheng Wang
    • 3
  • Igor Fedotov
    • 4
  1. 1.Research and Education Center “Materials”Don State Technical UniversityRostov-on-DonRussia
  2. 2.Research Institute of Mechanics and Applied MathematicsSouth Federal UniversityRostov-on-DonRussia
  3. 3.Institute of Engineering MechanicsBeijing Jiaotong UniversityBeijingChina
  4. 4.Department of Mathematical TechnologyTshwane University of TechnologyPretoriaSouth Africa

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