A block R of rubber is confined between plane parallel walls of a steel block (see figure).

Question:

A block R of rubber is confined between plane parallel walls of a steel block (see figure). A uniformly distributed pressure P0 is applied to the top of the rubber block by a force F.
(a) Derive a formula for the lateral pressure between the rubber and the steel. (Disregard friction between the rubber and the steel, and assume that the steel block is rigid when compared to the rubber.)
(b) Derive a formula for the dilatation of the rubber.
(c) Derive a formula for the strain-energy density of the rubber.