Thin inclusions in linear elasticity: a variational approach.

The inclusion of a very thin layer of very rigid material into a given elastic body has been widely considered, and in the classic literature (see for instance [9]) we find that when the Lame coefficients of the material in the layer grow s l /ε, where ε is the thickness of the layer, the problem becomes the inclusion of a plate (governed by an elliptic fourth-order equation) into the original elastic body.