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A mathematical approximation for the solution of a static indentation test

M A Haider1, M H Holmes

  • 1Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA.

Journal of Biomechanics
|July 1, 1997
PubMed
Summary

Researchers developed new mathematical approximations for the contact problem of indenting thin elastic layers. These closed-form solutions accurately predict deformation in static indentation tests, offering a simpler alternative to classical methods.

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Area of Science:

  • Solid Mechanics
  • Materials Science
  • Applied Mathematics

Background:

  • The classical contact problem involves indenting a thin, compressible, linear elastic layer bonded to a rigid substrate.
  • Accurate modeling of deformation is crucial for understanding material behavior under load.
  • Existing solutions often rely on complex integral transform methods.

Purpose of the Study:

  • To develop and present closed-form mathematical approximations for the indentation of elastic layers.
  • To analyze these approximations using static indentation tests.
  • To compare the new approximations with classical integral transform solutions.

Main Methods:

  • Derivation of closed-form mathematical approximations for plane and axisymmetric indentation.

Related Experiment Videos

  • Analysis of approximations through static indentation tests.
  • Comparison of predicted load values with classical integral transform solutions.

    • Main Results:

    • The new approximations accurately model the deformation of elastic layers during indentation.
    • For plane indentation, predictions agree within 2% relative error for specific aspect ratios and Poisson ratios.
    • Similar agreement was observed for the axisymmetric indentation case.

    Conclusions:

    • The developed closed-form approximations provide a simplified yet accurate method for analyzing static indentation problems.
    • This approach offers a practical alternative to complex integral transform solutions.
    • The approximations effectively capture the essential singular behavior in contact mechanics.