Summary
The problem of the indentation (without friction) of an absolutely rigid body into a thin elastic layer is investigated. It is assumed that the diameter of the contact area, which is unknown in advance, is large compared with the layer thickness. The inner asymptotic expansion for the contact pressure is obtained by means of the moment asymptotic expansion in the frame of the distributional theory of asymptotic expansions. The boundary layer is constructed using Alexandrov's method.
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Argatov, I.I. The pressure of a punch in the form of an elliptic paraboloid on a thin elastic layer. Acta Mechanica 180, 221–232 (2005). https://doi.org/10.1007/s00707-005-0217-3
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DOI: https://doi.org/10.1007/s00707-005-0217-3