Journal of Elasticity

, Volume 103, Issue 1, pp 15–52 | Cite as

Indentation of an Elastic Half-space by a Rigid Flat Punch as a Model Problem for Analysing Contact Problems with Coulomb Friction



One important problem which still remains to be solved today is the uniqueness of the solution of contact problems in linearized elastostatics with small Coulomb friction. This difficult question is addressed here in the case of the indentation of a two-dimensional elastic half-space by a rigid flat punch of finite width, which has been previously studied by Spence in Proc. Camb. Philos. Soc. 73, 249–268 (1973). It is proved that all the solutions have the same simple structure, involving active contact everywhere below the punch and a sticking interval surrounded by two inward slipping intervals. All these solutions show the same local asymptotics for surface traction and displacement at a border between a sticking and a slipping zone. These asymptotics describe (soft) singularities, which are universal (they hold with any geometry) and are explicitly given. It is also proved that in cases where the friction coefficient is small enough, the sticking intervals present in two distinct solutions, if two distinct solutions exist, cannot overlap.


Elasticity Contact Friction Uniqueness Singularity 

Mathematics Subject Classification (2000)

74B05 74M10 74M15 


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© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.CNRS – Laboratoire de Mécanique et d’AcoustiqueMarseille Cedex 20France
  2. 2.Mathematical InstituteAcademy of Sciences of the Czech RepublicPraha 1Czech Republic

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