Contact Interaction of an Axisymmetric Stamp and an Elastic Layer Fixed on a Poroelastic Base

The work presented is devoted to the axisymmetric contact problems on the interaction of a rigid stamp and an elastic layer fixed on a porous elastic half-space by using the Cowin–Nunziato model. It is assumed that the stamp basis has a flat or parabolic shape and friction is absent in the contact zone. With the help of the Hankel integral transform, the problems stated are reduced to solving integral equations for the unknown contact stress by using the collocation method. The values of contact stresses and the contact area in the case of a parabolic stamp are found. The normal stresses on the interface between the elastic layer and the poroelastic half-space are investigated. The relationship between the force acting on the stamp and the corresponding displacement, which is one of the main characteristics in determining the mechanical parameters of the material by the indentation method, is investigated. A comparative analysis of the values found for various parameters of the elastic layer and the poroelastic base is carried out. The numerical results are presented in a table and in the form of graphs.

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  1. 1.

    G. W. Nunziato and S. C. Cowin, “A nonlinear theory of elastic materials with voids,” Arch. Ration. Mech. Anal., 72, 175-201 (1979).

    Article  Google Scholar 

  2. 2.

    S. C. Cowin and G. W. Nunziato, “Linear theory of elastic materials with voids,” J. Elasticity, 13, 125-147 (1983).

    Article  Google Scholar 

  3. 3.

    A. Scalia and M. A. Sumbatyan, “Contact problem for porous elastic half-plane.,” J. Elasticity, 60, 91-102 (2000).

    Article  Google Scholar 

  4. 4.

    A. Scalia, “Contact problem for porous elastic strip,” Int. J. Eng. Sci., 40, 401-410 (2002).

    Article  Google Scholar 

  5. 5.

    D. Iesan and L. Nappa, “Axially symmetric problems for a porous elastic solid,” Int. J. Solids and Structures, 40, 5271-5286 (2003).

    Article  Google Scholar 

  6. 6.

    M. Repka, V. Sládek, and J. Sládek, “Numerical analysis of poroelastic materials described by the micro-dilatation theory,” Proc. Eng., 190, 248-254 (2017).

    Article  Google Scholar 

  7. 7.

    H. Ramézani, H. Steeb, and J. Jeong, “Analytical and numerical studies on penalized micro-dilatation (PMD) theory: Macro-micro link concept,” Europ. J. Mech. A/Solids, 34, July-August, 130-148 (2012).

  8. 8.

    M. Bırsan, “On the theory of elastic shells made from a material with voids,” Int. J. Solids and Structures, 43, 3106-3123 (2006).

    Article  Google Scholar 

  9. 9.

    G. Iovane and A. V. Nasedkin, “Modal analysis of piezoelectric bodies with voids. I. Mathematical approaches,” Appl. Math. Modelling, 34, 60-71 (2010).

    Article  Google Scholar 

  10. 10.

    G. Iovane and A. V. Nasedkin, “Finite element dynamic analysis of anisotropic elastic solids with voids.,” Computers and Structures, 87, 981-989 (2009).

    Article  Google Scholar 

  11. 11.

    G. Iovane and A. V. Nasedkin, “Finite element analysis of static problems for elastic media with voids,” Computers and Structures, 84, 19-24 (2005).

    Article  Google Scholar 

  12. 12.

    A. P. S. Selvadurai, “Stationary damage modelling of poroelastic contact,” Int. J. Solids and Structures, 41, 2043-2064 (2004).

    Article  Google Scholar 

  13. 13.

    A. P. S. Selvadurai and P. Samea, “On the indentation of a poroelastic halfspace,” Int. J. Eng. Sci., 149, 103246 (2020).

    Article  Google Scholar 

  14. 14.

    A. Lagzdins, A. Zilaucs, I. Beverte, J. Andersons, and U. Cabulis, “A refined strut model for describing the elastic properties of highly porous cellular polymers reinforced with short fibers,” Mech. Compos. Mater., 53, No. 3, 321-334 (2017).

    CAS  Article  Google Scholar 

  15. 15.

    N. B. Artamonova, S. V. Sheshenin, Yu. V. Frolova, O. Yu. Bessonova, and P. V. Novikov, “Calculating components of the effective tensors of elastic moduli and biot’s parameter of porous geocomposites,” Mech. Compos. Mater., 55, 715-726 (2020). https: //

  16. 16.

    Yu. M. Pleskachevskii, S. V. Shil’ko, and D. A. Chernous, “Structural modeling in the mechanics of porous materials,” Mechanics of Composite Materials., 39, 129-136 (2003). https: //

  17. 17.

    N. S. Bakhvalov, K. Yu. Bogachev, and M. E. Eglit, “Numerical calculation of effective elastic moduli for incompressible porous material,” Mech. Compos. Mater., 32, No. 5, 399-405 (1996). https: //

  18. 18.

    D. O. Butarovich, and A. A. Smirnov, “Modeling the mechanical properties of aluminum foam,” Vest. N. E. Bauman MGTU, Ser. Mashinostroenie, 76, No. 3, 123-131 (2009).

    Google Scholar 

  19. 19.

    V. S. Bondar, Yu. M. Temis, and M. V. Biryukov, “Determining the mechanical properties of aluminum foam at shock loading,” Izv. MGTU “MAMI,” 4, No. 4 (22), 11-14 (2014).

  20. 20.

    S. M. Belotserkovskii, and I. K. Lifanov, Numerical Methods in Singular Integral Equations and Their Application in Aerodynamics, Elasticity Theory and Electrodynamics [in Russian], M., Nauka (1985).

Download references

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Correspondence to M. I. Chebakov.

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Translated from Mekhanika Kompozitnykh Materialov, Vol. 56, No. 6, pp. 1113-1126, November-December, 2020.

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Chebakov, M.I., Kolosova, E.M. Contact Interaction of an Axisymmetric Stamp and an Elastic Layer Fixed on a Poroelastic Base. Mech Compos Mater 56, 769–778 (2021).

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  • contact problem
  • porous materials
  • poroelasticity
  • Cowin–Nunziato model
  • axisymmetric problem
  • elastic layer
  • collocation method
  • indentation