On a rigid inclusion pressed between two elastic half spaces

• We solve the problem of a rigid inclusion pressed between two elastic half spaces.
• A new distributed dislocation and Föppl integral approach is developed.
• The solution can be applied to cylindrical inclusions of arbitrary shape.
• The present approach does not experience any computational difficulties.
• Simplified solutions are also presented. All results are validated.

A solution to the problem of a rigid cylindrical inclusion pressed between two elastic half spaces is obtained using the distributed dislocation technique. The solution is compared with previously published analytical and numerical results for a rigid cylindrical inclusion bounded by two parabolic arcs with rounded corners. A simplified solution to the problem based on the classical contact theory and well-known results for crack problems is also suggested and validated. The simplified solution agrees well with analytical results in the case when the length of the opening around inclusion is much larger than the length of the contact zone.