Abstract
In this study, a three dimensional elastic problem for an inhomogeneous medium whose shear modulus G increases with coordinate variable z according to relation G (z)=G0 (1+z/a)m (G0, α and m are constants) is developed. In our previous paper, we derived the fundamental equations system for such inhomogeneous medium by using three kinds of displacement functions and applied them to determining the elastic stress distribution in a semi-infinite body subject to an arbitrary shaped distributed load (not necessarily axisymmetric) on its plane surface. In this paper, we apply these fundamental equations system to the inhomogeneous semi-infinite body whose plane surface is penetrated slowly by a rigid cylindrical punch of arbitrary shape. As an example, we consider the case where the inclined flat-ended cylinder indents the plane surface of the inhomogeneous semi-infinite body. Numerical calculations are carried out for several cases taking into account the variation in inhomogeneous elastic properties, and the numerical results for displacements, stress and stress intensity factor at the edge of the rigid punch are shown graphically.
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