The stresses and strains in a semi-infinite homogeneous body indented by a rigid sphere is a classical problem first investigated by Hertz. The special case of a thin elastic layer on a rigid substrate indented by a rigid sphere is considered here using a finite element approach. This is a problem of interest in the hardness testing of thin sheet material and in engineering design when the applied load is axially directed. When the applied load has a frictional (tangential) component, the results are of particular interest in tribology. The study is divided into two parts. The first considers purely axial loading while the second part, presented in a companion paper, considers a combination of axial and tangential loading. Results in both cases are compared with the well known Hertz solution.

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