Compression of Bonded Annular Rubber Blocks

The load-deflection relation and stress distribution of bonded annular rubber blocks are first derived by an approximate-linear approach. The solution approaches the exact relation asymptotically as the block thickness reduces. A general formula for the nonlinear load-deflection relation is then presented, based on a variational method, in which no specific form of the strain-energy function is required. An explicit approximate analytical solution is obtained by applying the general formula to a neo-Hookean material. The approximate solutions are compared with the finite-element analysis. The relationships among the stiffness, the shape factor s , and the diameter ratio β are explored in detail and some interesting phenomena are observed. For example, a centrally placed tiny hole in a very thin circular disk can cause a sharp drop in its stiffness.