ON A FLAT PUNCH INDENTING AN ELASTIC LAYER IN PLANE STRAIN
Suzanne Smith · The Quarterly Journal of Mathematics · 1964
BY making use of its limiting form for b/a → ∞ (b being the half-width of the punch and a the thickness of the layer), the exact solution is obtained, in terms of infinite eigenfunction expansions, for the problem of a punch indenting an elastic layer in plane strain when both the punch and the support for the elastic layer are smooth, rigid, and flat. Graphs of the stress on both surfaces of the elastic layer and of the deformation of the free surface are presented for various values of b/a. The analysis can be extended to other punch shapes, such as the wedge and parabolic punches, as well as to the axisymmetric punch problems for an elastic layer in which the area of contact between the punch and layer is a circle.