Mater.Phys.Mech.(MPM)
No 1/2, Vol. 28, 2016, pages 11-15

INDENTATION OF AN AXISYMMETRIC PUNCH INTO AN ELASTIC
TRANSVERSELY-ISOTROPIC HALF-SPACE WITH FUNCTIONALLY GRADED
TRANSVERSELY-ISOTROPIC COATING

A.S. Vasiliev, S.S. Volkov, S.M. Aizikovich

Abstract

Axisymmetric frictionless contact problem of the theory of elasticity on indentation of a non-deformable punch into an elastic transversely-isotropic half-space with transverselyisotropic functionally graded coating is considered. Elastic moduli of the coating vary with depth according to arbitrary function. The technique based on integral transformations is used to reduce the problems to the integral equation. Special approximations for the kernel transform is used to obtain analytical solution of the integral equations. The solution is asymptotically exact for both large and small values of geometric parameter of the problem (relative layer thickness). A method of construction the compliance functions is presented for a case of arbitrary axisymmetric normal and tangential loadings.

Keywords: contact problem of the theory of elasticity; an axisymmetric punch; an elastic transversely-isotropic half-space; transversely-isotropic functionally graded coating.

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