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An antiplane deformation of a functionally graded half-space

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Abstract

The problem about a pure shear of an elastic functionally graded half-space by a strip punch is considered. The half-space shear modulus grows exponentially by depth. The problem has been reduced to solution of an integral equation of the first kind with a difference kernel which was solved using asymptotic methods. The analysis of the contact stresses versus the shear modulus parameters is presented. The obtained relationships provide the basis for solution of an inverse problem for determining the functionally graded half-space shear modulus parameters as functions of the contact shear stress values. Also, it was shown that by choosing proper shear modulus parameters one can develop a sufficiently thick “approximately homogeneous” stress area inside of a functionally graded half-space.

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Acknowledgements

This research was supported by Ministry of Education and Science of the Russian Federation within the framework of the State Assignment (Grant Nos. 9.1481.2017/4.6, 9.4761.2017/6.7) and by Russian Foundation for Basic Research (Grant Nos. 17-07-01376-a, 16-07-00929-a).

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Correspondence to I. I. Kudish.

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Communicated by Victor Eremeyev and Holm Altenbach.

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Zelentsov, V.B., Lapina, P.A., Mitrin, B.I. et al. An antiplane deformation of a functionally graded half-space. Continuum Mech. Thermodyn. (2019). https://doi.org/10.1007/s00161-019-00783-1

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Keywords

  • Antiplane deformation
  • Shear
  • Functionally graded material
  • Contact stresses
  • Shear modulus