Summary: /. A&. Marhs Mechs, Vol. 65, No. 3, 4Y5-508,2001pp.
8 2001 Elsevier Science Ltd
All rights reserved. Printed in Great Britain
0021-8928/01/S--see front matter
THE PRESSURE OF A PUNCH IN THE FORM OF
AN ELLIPTIC PARABOLOID ON AN ELASTIC LAYER
OF FINITE THICKNESS/-
1. I. ARGATOV
(Received 29 August 2000)
The problem of the indentation (without friction) of an absolutely solid body into an elastic layer is investigated. It is assumed
that the diameter of the contact area which is unknown in advance, is small compared with the layer thickness. A model unilateral
contact problem of the pressure on the elastic half-space of a punch with a surface which is close to an elliptic paraboloid is
derived using the method of matched asymptotic expansions. The asymptotic solution of the model problem and the asymptotic
form of the boundary of the contact area are constructed using Nazarov's method. A uniformly valid asymptotic representation
is found for the density of the contact pressures. The asymptotic solution of the axisymmetric problem is written out in explicit
form. 0 2001 Elsevier Science Ltd. All rights reserved.